***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001943 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The sum of the squares of the hook lengths of an integer partition. For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(la): return sum(h^2 for h in la.hooks()) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 5 [1,1] => 5 [3] => 14 [2,1] => 11 [1,1,1] => 14 [4] => 30 [3,1] => 22 [2,2] => 18 [2,1,1] => 22 [1,1,1,1] => 30 [5] => 55 [4,1] => 40 [3,2] => 31 [3,1,1] => 35 [2,2,1] => 31 [2,1,1,1] => 40 [1,1,1,1,1] => 55 [6] => 91 [5,1] => 67 [4,2] => 51 [4,1,1] => 55 [3,3] => 43 [3,2,1] => 46 [3,1,1,1] => 55 [2,2,2] => 43 [2,2,1,1] => 51 [2,1,1,1,1] => 67 [1,1,1,1,1,1] => 91 [7] => 140 [6,1] => 105 [5,2] => 80 [5,1,1] => 84 [4,3] => 65 [4,2,1] => 68 [4,1,1,1] => 77 [3,3,1] => 60 [3,2,2] => 60 [3,2,1,1] => 68 [3,1,1,1,1] => 84 [2,2,2,1] => 65 [2,2,1,1,1] => 80 [2,1,1,1,1,1] => 105 [1,1,1,1,1,1,1] => 140 [8] => 204 [7,1] => 156 [6,2] => 120 [6,1,1] => 124 [5,3] => 96 [5,2,1] => 99 [5,1,1,1] => 108 [4,4] => 84 [4,3,1] => 84 [4,2,2] => 84 [4,2,1,1] => 92 [4,1,1,1,1] => 108 [3,3,2] => 76 [3,3,1,1] => 84 [3,2,2,1] => 84 [3,2,1,1,1] => 99 [3,1,1,1,1,1] => 124 [2,2,2,2] => 84 [2,2,2,1,1] => 96 [2,2,1,1,1,1] => 120 [2,1,1,1,1,1,1] => 156 [1,1,1,1,1,1,1,1] => 204 [9] => 285 [8,1] => 222 [7,2] => 173 [7,1,1] => 177 [6,3] => 138 [6,2,1] => 141 [6,1,1,1] => 150 [5,4] => 117 [5,3,1] => 117 [5,2,2] => 117 [5,2,1,1] => 125 [5,1,1,1,1] => 141 [4,4,1] => 105 [4,3,2] => 102 [4,3,1,1] => 110 [4,2,2,1] => 110 [4,2,1,1,1] => 125 [4,1,1,1,1,1] => 150 [3,3,3] => 93 [3,3,2,1] => 102 [3,3,1,1,1] => 117 [3,2,2,2] => 105 [3,2,2,1,1] => 117 [3,2,1,1,1,1] => 141 [3,1,1,1,1,1,1] => 177 [2,2,2,2,1] => 117 [2,2,2,1,1,1] => 138 [2,2,1,1,1,1,1] => 173 [2,1,1,1,1,1,1,1] => 222 [1,1,1,1,1,1,1,1,1] => 285 [10] => 385 [9,1] => 305 [8,2] => 241 [8,1,1] => 245 [7,3] => 193 [7,2,1] => 196 [7,1,1,1] => 205 [6,4] => 161 [6,3,1] => 161 [6,2,2] => 161 [6,2,1,1] => 169 [6,1,1,1,1] => 185 [5,5] => 145 [5,4,1] => 140 [5,3,2] => 137 [5,3,1,1] => 145 [5,2,2,1] => 145 [5,2,1,1,1] => 160 [5,1,1,1,1,1] => 185 [4,4,2] => 125 [4,4,1,1] => 133 [4,3,3] => 121 [4,3,2,1] => 130 [4,3,1,1,1] => 145 [4,2,2,2] => 133 [4,2,2,1,1] => 145 [4,2,1,1,1,1] => 169 [4,1,1,1,1,1,1] => 205 [3,3,3,1] => 121 [3,3,2,2] => 125 [3,3,2,1,1] => 137 [3,3,1,1,1,1] => 161 [3,2,2,2,1] => 140 [3,2,2,1,1,1] => 161 [3,2,1,1,1,1,1] => 196 [3,1,1,1,1,1,1,1] => 245 [2,2,2,2,2] => 145 [2,2,2,2,1,1] => 161 [2,2,2,1,1,1,1] => 193 [2,2,1,1,1,1,1,1] => 241 [2,1,1,1,1,1,1,1,1] => 305 [1,1,1,1,1,1,1,1,1,1] => 385 [11] => 506 [10,1] => 407 [9,2] => 326 [9,1,1] => 330 [8,3] => 263 [8,2,1] => 266 [8,1,1,1] => 275 [7,4] => 218 [7,3,1] => 218 [7,2,2] => 218 [7,2,1,1] => 226 [7,1,1,1,1] => 242 [6,5] => 191 [6,4,1] => 186 [6,3,2] => 183 [6,3,1,1] => 191 [6,2,2,1] => 191 [6,2,1,1,1] => 206 [6,1,1,1,1,1] => 231 [5,5,1] => 170 [5,4,2] => 162 [5,4,1,1] => 170 [5,3,3] => 158 [5,3,2,1] => 167 [5,3,1,1,1] => 182 [5,2,2,2] => 170 [5,2,2,1,1] => 182 [5,2,1,1,1,1] => 206 [5,1,1,1,1,1,1] => 242 [4,4,3] => 146 [4,4,2,1] => 155 [4,4,1,1,1] => 170 [4,3,3,1] => 151 [4,3,2,2] => 155 [4,3,2,1,1] => 167 [4,3,1,1,1,1] => 191 [4,2,2,2,1] => 170 [4,2,2,1,1,1] => 191 [4,2,1,1,1,1,1] => 226 [4,1,1,1,1,1,1,1] => 275 [3,3,3,2] => 146 [3,3,3,1,1] => 158 [3,3,2,2,1] => 162 [3,3,2,1,1,1] => 183 [3,3,1,1,1,1,1] => 218 [3,2,2,2,2] => 170 [3,2,2,2,1,1] => 186 [3,2,2,1,1,1,1] => 218 [3,2,1,1,1,1,1,1] => 266 [3,1,1,1,1,1,1,1,1] => 330 [2,2,2,2,2,1] => 191 [2,2,2,2,1,1,1] => 218 [2,2,2,1,1,1,1,1] => 263 [2,2,1,1,1,1,1,1,1] => 326 [2,1,1,1,1,1,1,1,1,1] => 407 [1,1,1,1,1,1,1,1,1,1,1] => 506 [12] => 650 [11,1] => 530 [10,2] => 430 [10,1,1] => 434 [9,3] => 350 [9,2,1] => 353 [9,1,1,1] => 362 [8,4] => 290 [8,3,1] => 290 [8,2,2] => 290 [8,2,1,1] => 298 [8,1,1,1,1] => 314 [7,5] => 250 [7,4,1] => 245 [7,3,2] => 242 [7,3,1,1] => 250 [7,2,2,1] => 250 [7,2,1,1,1] => 265 [7,1,1,1,1,1] => 290 [6,6] => 230 [6,5,1] => 218 [6,4,2] => 210 [6,4,1,1] => 218 [6,3,3] => 206 [6,3,2,1] => 215 [6,3,1,1,1] => 230 [6,2,2,2] => 218 [6,2,2,1,1] => 230 [6,2,1,1,1,1] => 254 [6,1,1,1,1,1,1] => 290 [5,5,2] => 194 [5,5,1,1] => 202 [5,4,3] => 185 [5,4,2,1] => 194 [5,4,1,1,1] => 209 [5,3,3,1] => 190 [5,3,2,2] => 194 [5,3,2,1,1] => 206 [5,3,1,1,1,1] => 230 [5,2,2,2,1] => 209 [5,2,2,1,1,1] => 230 [5,2,1,1,1,1,1] => 265 [5,1,1,1,1,1,1,1] => 314 [4,4,4] => 170 [4,4,3,1] => 178 [4,4,2,2] => 182 [4,4,2,1,1] => 194 [4,4,1,1,1,1] => 218 [4,3,3,2] => 178 [4,3,3,1,1] => 190 [4,3,2,2,1] => 194 [4,3,2,1,1,1] => 215 [4,3,1,1,1,1,1] => 250 [4,2,2,2,2] => 202 [4,2,2,2,1,1] => 218 [4,2,2,1,1,1,1] => 250 [4,2,1,1,1,1,1,1] => 298 [4,1,1,1,1,1,1,1,1] => 362 [3,3,3,3] => 170 [3,3,3,2,1] => 185 [3,3,3,1,1,1] => 206 [3,3,2,2,2] => 194 [3,3,2,2,1,1] => 210 [3,3,2,1,1,1,1] => 242 [3,3,1,1,1,1,1,1] => 290 [3,2,2,2,2,1] => 218 [3,2,2,2,1,1,1] => 245 [3,2,2,1,1,1,1,1] => 290 [3,2,1,1,1,1,1,1,1] => 353 [3,1,1,1,1,1,1,1,1,1] => 434 [2,2,2,2,2,2] => 230 [2,2,2,2,2,1,1] => 250 [2,2,2,2,1,1,1,1] => 290 [2,2,2,1,1,1,1,1,1] => 350 [2,2,1,1,1,1,1,1,1,1] => 430 [2,1,1,1,1,1,1,1,1,1,1] => 530 [1,1,1,1,1,1,1,1,1,1,1,1] => 650 [13] => 819 [12,1] => 676 [11,2] => 555 [11,1,1] => 559 [10,3] => 456 [10,2,1] => 459 [10,1,1,1] => 468 [9,4] => 379 [9,3,1] => 379 [9,2,2] => 379 [9,2,1,1] => 387 [9,1,1,1,1] => 403 [8,5] => 324 [8,4,1] => 319 [8,3,2] => 316 [8,3,1,1] => 324 [8,2,2,1] => 324 [8,2,1,1,1] => 339 [8,1,1,1,1,1] => 364 [7,6] => 291 [7,5,1] => 279 [7,4,2] => 271 [7,4,1,1] => 279 [7,3,3] => 267 [7,3,2,1] => 276 [7,3,1,1,1] => 291 [7,2,2,2] => 279 [7,2,2,1,1] => 291 [7,2,1,1,1,1] => 315 [7,1,1,1,1,1,1] => 351 [6,6,1] => 259 [6,5,2] => 244 [6,5,1,1] => 252 [6,4,3] => 235 [6,4,2,1] => 244 [6,4,1,1,1] => 259 [6,3,3,1] => 240 [6,3,2,2] => 244 [6,3,2,1,1] => 256 [6,3,1,1,1,1] => 280 [6,2,2,2,1] => 259 [6,2,2,1,1,1] => 280 [6,2,1,1,1,1,1] => 315 [6,1,1,1,1,1,1,1] => 364 [5,5,3] => 219 [5,5,2,1] => 228 [5,5,1,1,1] => 243 [5,4,4] => 211 [5,4,3,1] => 219 [5,4,2,2] => 223 [5,4,2,1,1] => 235 [5,4,1,1,1,1] => 259 [5,3,3,2] => 219 [5,3,3,1,1] => 231 [5,3,2,2,1] => 235 [5,3,2,1,1,1] => 256 [5,3,1,1,1,1,1] => 291 [5,2,2,2,2] => 243 [5,2,2,2,1,1] => 259 [5,2,2,1,1,1,1] => 291 [5,2,1,1,1,1,1,1] => 339 [5,1,1,1,1,1,1,1,1] => 403 [4,4,4,1] => 204 [4,4,3,2] => 207 [4,4,3,1,1] => 219 [4,4,2,2,1] => 223 [4,4,2,1,1,1] => 244 [4,4,1,1,1,1,1] => 279 [4,3,3,3] => 204 [4,3,3,2,1] => 219 [4,3,3,1,1,1] => 240 [4,3,2,2,2] => 228 [4,3,2,2,1,1] => 244 [4,3,2,1,1,1,1] => 276 [4,3,1,1,1,1,1,1] => 324 [4,2,2,2,2,1] => 252 [4,2,2,2,1,1,1] => 279 [4,2,2,1,1,1,1,1] => 324 [4,2,1,1,1,1,1,1,1] => 387 [4,1,1,1,1,1,1,1,1,1] => 468 [3,3,3,3,1] => 211 [3,3,3,2,2] => 219 [3,3,3,2,1,1] => 235 [3,3,3,1,1,1,1] => 267 [3,3,2,2,2,1] => 244 [3,3,2,2,1,1,1] => 271 [3,3,2,1,1,1,1,1] => 316 [3,3,1,1,1,1,1,1,1] => 379 [3,2,2,2,2,2] => 259 [3,2,2,2,2,1,1] => 279 [3,2,2,2,1,1,1,1] => 319 [3,2,2,1,1,1,1,1,1] => 379 [3,2,1,1,1,1,1,1,1,1] => 459 [3,1,1,1,1,1,1,1,1,1,1] => 559 [2,2,2,2,2,2,1] => 291 [2,2,2,2,2,1,1,1] => 324 [2,2,2,2,1,1,1,1,1] => 379 [2,2,2,1,1,1,1,1,1,1] => 456 [2,2,1,1,1,1,1,1,1,1,1] => 555 [2,1,1,1,1,1,1,1,1,1,1,1] => 676 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 819 [14] => 1015 [13,1] => 847 [12,2] => 703 [12,1,1] => 707 [11,3] => 583 [11,2,1] => 586 [11,1,1,1] => 595 [10,4] => 487 [10,3,1] => 487 [10,2,2] => 487 [10,2,1,1] => 495 [10,1,1,1,1] => 511 [9,5] => 415 [9,4,1] => 410 [9,3,2] => 407 [9,3,1,1] => 415 [9,2,2,1] => 415 [9,2,1,1,1] => 430 [9,1,1,1,1,1] => 455 [8,6] => 367 [8,5,1] => 355 [8,4,2] => 347 [8,4,1,1] => 355 [8,3,3] => 343 [8,3,2,1] => 352 [8,3,1,1,1] => 367 [8,2,2,2] => 355 [8,2,2,1,1] => 367 [8,2,1,1,1,1] => 391 [8,1,1,1,1,1,1] => 427 [7,7] => 343 [7,6,1] => 322 [7,5,2] => 307 [7,5,1,1] => 315 [7,4,3] => 298 [7,4,2,1] => 307 [7,4,1,1,1] => 322 [7,3,3,1] => 303 [7,3,2,2] => 307 [7,3,2,1,1] => 319 [7,3,1,1,1,1] => 343 [7,2,2,2,1] => 322 [7,2,2,1,1,1] => 343 [7,2,1,1,1,1,1] => 378 [7,1,1,1,1,1,1,1] => 427 [6,6,2] => 287 [6,6,1,1] => 295 [6,5,3] => 271 [6,5,2,1] => 280 [6,5,1,1,1] => 295 [6,4,4] => 263 [6,4,3,1] => 271 [6,4,2,2] => 275 [6,4,2,1,1] => 287 [6,4,1,1,1,1] => 311 [6,3,3,2] => 271 [6,3,3,1,1] => 283 [6,3,2,2,1] => 287 [6,3,2,1,1,1] => 308 [6,3,1,1,1,1,1] => 343 [6,2,2,2,2] => 295 [6,2,2,2,1,1] => 311 [6,2,2,1,1,1,1] => 343 [6,2,1,1,1,1,1,1] => 391 [6,1,1,1,1,1,1,1,1] => 455 [5,5,4] => 247 [5,5,3,1] => 255 [5,5,2,2] => 259 [5,5,2,1,1] => 271 [5,5,1,1,1,1] => 295 [5,4,4,1] => 247 [5,4,3,2] => 250 [5,4,3,1,1] => 262 [5,4,2,2,1] => 266 [5,4,2,1,1,1] => 287 [5,4,1,1,1,1,1] => 322 [5,3,3,3] => 247 [5,3,3,2,1] => 262 [5,3,3,1,1,1] => 283 [5,3,2,2,2] => 271 [5,3,2,2,1,1] => 287 [5,3,2,1,1,1,1] => 319 [5,3,1,1,1,1,1,1] => 367 [5,2,2,2,2,1] => 295 [5,2,2,2,1,1,1] => 322 [5,2,2,1,1,1,1,1] => 367 [5,2,1,1,1,1,1,1,1] => 430 [5,1,1,1,1,1,1,1,1,1] => 511 [4,4,4,2] => 235 [4,4,4,1,1] => 247 [4,4,3,3] => 235 [4,4,3,2,1] => 250 [4,4,3,1,1,1] => 271 [4,4,2,2,2] => 259 [4,4,2,2,1,1] => 275 [4,4,2,1,1,1,1] => 307 [4,4,1,1,1,1,1,1] => 355 [4,3,3,3,1] => 247 [4,3,3,2,2] => 255 [4,3,3,2,1,1] => 271 [4,3,3,1,1,1,1] => 303 [4,3,2,2,2,1] => 280 [4,3,2,2,1,1,1] => 307 [4,3,2,1,1,1,1,1] => 352 [4,3,1,1,1,1,1,1,1] => 415 [4,2,2,2,2,2] => 295 [4,2,2,2,2,1,1] => 315 [4,2,2,2,1,1,1,1] => 355 [4,2,2,1,1,1,1,1,1] => 415 [4,2,1,1,1,1,1,1,1,1] => 495 [4,1,1,1,1,1,1,1,1,1,1] => 595 [3,3,3,3,2] => 247 [3,3,3,3,1,1] => 263 [3,3,3,2,2,1] => 271 [3,3,3,2,1,1,1] => 298 [3,3,3,1,1,1,1,1] => 343 [3,3,2,2,2,2] => 287 [3,3,2,2,2,1,1] => 307 [3,3,2,2,1,1,1,1] => 347 [3,3,2,1,1,1,1,1,1] => 407 [3,3,1,1,1,1,1,1,1,1] => 487 [3,2,2,2,2,2,1] => 322 [3,2,2,2,2,1,1,1] => 355 [3,2,2,2,1,1,1,1,1] => 410 [3,2,2,1,1,1,1,1,1,1] => 487 [3,2,1,1,1,1,1,1,1,1,1] => 586 [3,1,1,1,1,1,1,1,1,1,1,1] => 707 [2,2,2,2,2,2,2] => 343 [2,2,2,2,2,2,1,1] => 367 [2,2,2,2,2,1,1,1,1] => 415 [2,2,2,2,1,1,1,1,1,1] => 487 [2,2,2,1,1,1,1,1,1,1,1] => 583 [2,2,1,1,1,1,1,1,1,1,1,1] => 703 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 847 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1015 [15] => 1240 [14,1] => 1045 [13,2] => 876 [13,1,1] => 880 [12,3] => 733 [12,2,1] => 736 [12,1,1,1] => 745 [11,4] => 616 [11,3,1] => 616 [11,2,2] => 616 [11,2,1,1] => 624 [11,1,1,1,1] => 640 [10,5] => 525 [10,4,1] => 520 [10,3,2] => 517 [10,3,1,1] => 525 [10,2,2,1] => 525 [10,2,1,1,1] => 540 [10,1,1,1,1,1] => 565 [9,6] => 460 [9,5,1] => 448 [9,4,2] => 440 [9,4,1,1] => 448 [9,3,3] => 436 [9,3,2,1] => 445 [9,3,1,1,1] => 460 [9,2,2,2] => 448 [9,2,2,1,1] => 460 [9,2,1,1,1,1] => 484 [9,1,1,1,1,1,1] => 520 [8,7] => 421 [8,6,1] => 400 [8,5,2] => 385 [8,5,1,1] => 393 [8,4,3] => 376 [8,4,2,1] => 385 [8,4,1,1,1] => 400 [8,3,3,1] => 381 [8,3,2,2] => 385 [8,3,2,1,1] => 397 [8,3,1,1,1,1] => 421 [8,2,2,2,1] => 400 [8,2,2,1,1,1] => 421 [8,2,1,1,1,1,1] => 456 [8,1,1,1,1,1,1,1] => 505 [7,7,1] => 376 [7,6,2] => 352 [7,6,1,1] => 360 [7,5,3] => 336 [7,5,2,1] => 345 [7,5,1,1,1] => 360 [7,4,4] => 328 [7,4,3,1] => 336 [7,4,2,2] => 340 [7,4,2,1,1] => 352 [7,4,1,1,1,1] => 376 [7,3,3,2] => 336 [7,3,3,1,1] => 348 [7,3,2,2,1] => 352 [7,3,2,1,1,1] => 373 [7,3,1,1,1,1,1] => 408 [7,2,2,2,2] => 360 [7,2,2,2,1,1] => 376 [7,2,2,1,1,1,1] => 408 [7,2,1,1,1,1,1,1] => 456 [7,1,1,1,1,1,1,1,1] => 520 [6,6,3] => 316 [6,6,2,1] => 325 [6,6,1,1,1] => 340 [6,5,4] => 301 [6,5,3,1] => 309 [6,5,2,2] => 313 [6,5,2,1,1] => 325 [6,5,1,1,1,1] => 349 [6,4,4,1] => 301 [6,4,3,2] => 304 [6,4,3,1,1] => 316 [6,4,2,2,1] => 320 [6,4,2,1,1,1] => 341 [6,4,1,1,1,1,1] => 376 [6,3,3,3] => 301 [6,3,3,2,1] => 316 [6,3,3,1,1,1] => 337 [6,3,2,2,2] => 325 [6,3,2,2,1,1] => 341 [6,3,2,1,1,1,1] => 373 [6,3,1,1,1,1,1,1] => 421 [6,2,2,2,2,1] => 349 [6,2,2,2,1,1,1] => 376 [6,2,2,1,1,1,1,1] => 421 [6,2,1,1,1,1,1,1,1] => 484 [6,1,1,1,1,1,1,1,1,1] => 565 [5,5,5] => 280 [5,5,4,1] => 285 [5,5,3,2] => 288 [5,5,3,1,1] => 300 [5,5,2,2,1] => 304 [5,5,2,1,1,1] => 325 [5,5,1,1,1,1,1] => 360 [5,4,4,2] => 280 [5,4,4,1,1] => 292 [5,4,3,3] => 280 [5,4,3,2,1] => 295 [5,4,3,1,1,1] => 316 [5,4,2,2,2] => 304 [5,4,2,2,1,1] => 320 [5,4,2,1,1,1,1] => 352 [5,4,1,1,1,1,1,1] => 400 [5,3,3,3,1] => 292 [5,3,3,2,2] => 300 [5,3,3,2,1,1] => 316 [5,3,3,1,1,1,1] => 348 [5,3,2,2,2,1] => 325 [5,3,2,2,1,1,1] => 352 [5,3,2,1,1,1,1,1] => 397 [5,3,1,1,1,1,1,1,1] => 460 [5,2,2,2,2,2] => 340 [5,2,2,2,2,1,1] => 360 [5,2,2,2,1,1,1,1] => 400 [5,2,2,1,1,1,1,1,1] => 460 [5,2,1,1,1,1,1,1,1,1] => 540 [5,1,1,1,1,1,1,1,1,1,1] => 640 [4,4,4,3] => 265 [4,4,4,2,1] => 280 [4,4,4,1,1,1] => 301 [4,4,3,3,1] => 280 [4,4,3,2,2] => 288 [4,4,3,2,1,1] => 304 [4,4,3,1,1,1,1] => 336 [4,4,2,2,2,1] => 313 [4,4,2,2,1,1,1] => 340 [4,4,2,1,1,1,1,1] => 385 [4,4,1,1,1,1,1,1,1] => 448 [4,3,3,3,2] => 285 [4,3,3,3,1,1] => 301 [4,3,3,2,2,1] => 309 [4,3,3,2,1,1,1] => 336 [4,3,3,1,1,1,1,1] => 381 [4,3,2,2,2,2] => 325 [4,3,2,2,2,1,1] => 345 [4,3,2,2,1,1,1,1] => 385 [4,3,2,1,1,1,1,1,1] => 445 [4,3,1,1,1,1,1,1,1,1] => 525 [4,2,2,2,2,2,1] => 360 [4,2,2,2,2,1,1,1] => 393 [4,2,2,2,1,1,1,1,1] => 448 [4,2,2,1,1,1,1,1,1,1] => 525 [4,2,1,1,1,1,1,1,1,1,1] => 624 [4,1,1,1,1,1,1,1,1,1,1,1] => 745 [3,3,3,3,3] => 280 [3,3,3,3,2,1] => 301 [3,3,3,3,1,1,1] => 328 [3,3,3,2,2,2] => 316 [3,3,3,2,2,1,1] => 336 [3,3,3,2,1,1,1,1] => 376 [3,3,3,1,1,1,1,1,1] => 436 [3,3,2,2,2,2,1] => 352 [3,3,2,2,2,1,1,1] => 385 [3,3,2,2,1,1,1,1,1] => 440 [3,3,2,1,1,1,1,1,1,1] => 517 [3,3,1,1,1,1,1,1,1,1,1] => 616 [3,2,2,2,2,2,2] => 376 [3,2,2,2,2,2,1,1] => 400 [3,2,2,2,2,1,1,1,1] => 448 [3,2,2,2,1,1,1,1,1,1] => 520 [3,2,2,1,1,1,1,1,1,1,1] => 616 [3,2,1,1,1,1,1,1,1,1,1,1] => 736 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 880 [2,2,2,2,2,2,2,1] => 421 [2,2,2,2,2,2,1,1,1] => 460 [2,2,2,2,2,1,1,1,1,1] => 525 [2,2,2,2,1,1,1,1,1,1,1] => 616 [2,2,2,1,1,1,1,1,1,1,1,1] => 733 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 876 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1045 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1240 [16] => 1496 [15,1] => 1272 [14,2] => 1076 [14,1,1] => 1080 [13,3] => 908 [13,2,1] => 911 [13,1,1,1] => 920 [12,4] => 768 [12,3,1] => 768 [12,2,2] => 768 [12,2,1,1] => 776 [12,1,1,1,1] => 792 [11,5] => 656 [11,4,1] => 651 [11,3,2] => 648 [11,3,1,1] => 656 [11,2,2,1] => 656 [11,2,1,1,1] => 671 [11,1,1,1,1,1] => 696 [10,6] => 572 [10,5,1] => 560 [10,4,2] => 552 [10,4,1,1] => 560 [10,3,3] => 548 [10,3,2,1] => 557 [10,3,1,1,1] => 572 [10,2,2,2] => 560 [10,2,2,1,1] => 572 [10,2,1,1,1,1] => 596 [10,1,1,1,1,1,1] => 632 [9,7] => 516 [9,6,1] => 495 [9,5,2] => 480 [9,5,1,1] => 488 [9,4,3] => 471 [9,4,2,1] => 480 [9,4,1,1,1] => 495 [9,3,3,1] => 476 [9,3,2,2] => 480 [9,3,2,1,1] => 492 [9,3,1,1,1,1] => 516 [9,2,2,2,1] => 495 [9,2,2,1,1,1] => 516 [9,2,1,1,1,1,1] => 551 [9,1,1,1,1,1,1,1] => 600 [8,8] => 488 [8,7,1] => 456 [8,6,2] => 432 [8,6,1,1] => 440 [8,5,3] => 416 [8,5,2,1] => 425 [8,5,1,1,1] => 440 [8,4,4] => 408 [8,4,3,1] => 416 [8,4,2,2] => 420 [8,4,2,1,1] => 432 [8,4,1,1,1,1] => 456 [8,3,3,2] => 416 [8,3,3,1,1] => 428 [8,3,2,2,1] => 432 [8,3,2,1,1,1] => 453 [8,3,1,1,1,1,1] => 488 [8,2,2,2,2] => 440 [8,2,2,2,1,1] => 456 [8,2,2,1,1,1,1] => 488 [8,2,1,1,1,1,1,1] => 536 [8,1,1,1,1,1,1,1,1] => 600 [7,7,2] => 408 [7,7,1,1] => 416 [7,6,3] => 383 [7,6,2,1] => 392 [7,6,1,1,1] => 407 [7,5,4] => 368 [7,5,3,1] => 376 [7,5,2,2] => 380 [7,5,2,1,1] => 392 [7,5,1,1,1,1] => 416 [7,4,4,1] => 368 [7,4,3,2] => 371 [7,4,3,1,1] => 383 [7,4,2,2,1] => 387 [7,4,2,1,1,1] => 408 [7,4,1,1,1,1,1] => 443 [7,3,3,3] => 368 [7,3,3,2,1] => 383 [7,3,3,1,1,1] => 404 [7,3,2,2,2] => 392 [7,3,2,2,1,1] => 408 [7,3,2,1,1,1,1] => 440 [7,3,1,1,1,1,1,1] => 488 [7,2,2,2,2,1] => 416 [7,2,2,2,1,1,1] => 443 [7,2,2,1,1,1,1,1] => 488 [7,2,1,1,1,1,1,1,1] => 551 [7,1,1,1,1,1,1,1,1,1] => 632 [6,6,4] => 348 [6,6,3,1] => 356 [6,6,2,2] => 360 [6,6,2,1,1] => 372 [6,6,1,1,1,1] => 396 [6,5,5] => 336 [6,5,4,1] => 341 [6,5,3,2] => 344 [6,5,3,1,1] => 356 [6,5,2,2,1] => 360 [6,5,2,1,1,1] => 381 [6,5,1,1,1,1,1] => 416 [6,4,4,2] => 336 [6,4,4,1,1] => 348 [6,4,3,3] => 336 [6,4,3,2,1] => 351 [6,4,3,1,1,1] => 372 [6,4,2,2,2] => 360 [6,4,2,2,1,1] => 376 [6,4,2,1,1,1,1] => 408 [6,4,1,1,1,1,1,1] => 456 [6,3,3,3,1] => 348 [6,3,3,2,2] => 356 [6,3,3,2,1,1] => 372 [6,3,3,1,1,1,1] => 404 [6,3,2,2,2,1] => 381 [6,3,2,2,1,1,1] => 408 [6,3,2,1,1,1,1,1] => 453 [6,3,1,1,1,1,1,1,1] => 516 [6,2,2,2,2,2] => 396 [6,2,2,2,2,1,1] => 416 [6,2,2,2,1,1,1,1] => 456 [6,2,2,1,1,1,1,1,1] => 516 [6,2,1,1,1,1,1,1,1,1] => 596 [6,1,1,1,1,1,1,1,1,1,1] => 696 [5,5,5,1] => 320 [5,5,4,2] => 320 [5,5,4,1,1] => 332 [5,5,3,3] => 320 [5,5,3,2,1] => 335 [5,5,3,1,1,1] => 356 [5,5,2,2,2] => 344 [5,5,2,2,1,1] => 360 [5,5,2,1,1,1,1] => 392 [5,5,1,1,1,1,1,1] => 440 [5,4,4,3] => 312 [5,4,4,2,1] => 327 [5,4,4,1,1,1] => 348 [5,4,3,3,1] => 327 [5,4,3,2,2] => 335 [5,4,3,2,1,1] => 351 [5,4,3,1,1,1,1] => 383 [5,4,2,2,2,1] => 360 [5,4,2,2,1,1,1] => 387 [5,4,2,1,1,1,1,1] => 432 [5,4,1,1,1,1,1,1,1] => 495 [5,3,3,3,2] => 332 [5,3,3,3,1,1] => 348 [5,3,3,2,2,1] => 356 [5,3,3,2,1,1,1] => 383 [5,3,3,1,1,1,1,1] => 428 [5,3,2,2,2,2] => 372 [5,3,2,2,2,1,1] => 392 [5,3,2,2,1,1,1,1] => 432 [5,3,2,1,1,1,1,1,1] => 492 [5,3,1,1,1,1,1,1,1,1] => 572 [5,2,2,2,2,2,1] => 407 [5,2,2,2,2,1,1,1] => 440 [5,2,2,2,1,1,1,1,1] => 495 [5,2,2,1,1,1,1,1,1,1] => 572 [5,2,1,1,1,1,1,1,1,1,1] => 671 [5,1,1,1,1,1,1,1,1,1,1,1] => 792 [4,4,4,4] => 296 [4,4,4,3,1] => 312 [4,4,4,2,2] => 320 [4,4,4,2,1,1] => 336 [4,4,4,1,1,1,1] => 368 [4,4,3,3,2] => 320 [4,4,3,3,1,1] => 336 [4,4,3,2,2,1] => 344 [4,4,3,2,1,1,1] => 371 [4,4,3,1,1,1,1,1] => 416 [4,4,2,2,2,2] => 360 [4,4,2,2,2,1,1] => 380 [4,4,2,2,1,1,1,1] => 420 [4,4,2,1,1,1,1,1,1] => 480 [4,4,1,1,1,1,1,1,1,1] => 560 [4,3,3,3,3] => 320 [4,3,3,3,2,1] => 341 [4,3,3,3,1,1,1] => 368 [4,3,3,2,2,2] => 356 [4,3,3,2,2,1,1] => 376 [4,3,3,2,1,1,1,1] => 416 [4,3,3,1,1,1,1,1,1] => 476 [4,3,2,2,2,2,1] => 392 [4,3,2,2,2,1,1,1] => 425 [4,3,2,2,1,1,1,1,1] => 480 [4,3,2,1,1,1,1,1,1,1] => 557 [4,3,1,1,1,1,1,1,1,1,1] => 656 [4,2,2,2,2,2,2] => 416 [4,2,2,2,2,2,1,1] => 440 [4,2,2,2,2,1,1,1,1] => 488 [4,2,2,2,1,1,1,1,1,1] => 560 [4,2,2,1,1,1,1,1,1,1,1] => 656 [4,2,1,1,1,1,1,1,1,1,1,1] => 776 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 920 [3,3,3,3,3,1] => 336 [3,3,3,3,2,2] => 348 [3,3,3,3,2,1,1] => 368 [3,3,3,3,1,1,1,1] => 408 [3,3,3,2,2,2,1] => 383 [3,3,3,2,2,1,1,1] => 416 [3,3,3,2,1,1,1,1,1] => 471 [3,3,3,1,1,1,1,1,1,1] => 548 [3,3,2,2,2,2,2] => 408 [3,3,2,2,2,2,1,1] => 432 [3,3,2,2,2,1,1,1,1] => 480 [3,3,2,2,1,1,1,1,1,1] => 552 [3,3,2,1,1,1,1,1,1,1,1] => 648 [3,3,1,1,1,1,1,1,1,1,1,1] => 768 [3,2,2,2,2,2,2,1] => 456 [3,2,2,2,2,2,1,1,1] => 495 [3,2,2,2,2,1,1,1,1,1] => 560 [3,2,2,2,1,1,1,1,1,1,1] => 651 [3,2,2,1,1,1,1,1,1,1,1,1] => 768 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 911 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1080 [2,2,2,2,2,2,2,2] => 488 [2,2,2,2,2,2,2,1,1] => 516 [2,2,2,2,2,2,1,1,1,1] => 572 [2,2,2,2,2,1,1,1,1,1,1] => 656 [2,2,2,2,1,1,1,1,1,1,1,1] => 768 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 908 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 1076 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1272 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1496 [17] => 1785 [16,1] => 1530 [15,2] => 1305 [15,1,1] => 1309 [14,3] => 1110 [14,2,1] => 1113 [14,1,1,1] => 1122 [13,4] => 945 [13,3,1] => 945 [13,2,2] => 945 [13,2,1,1] => 953 [13,1,1,1,1] => 969 [12,5] => 810 [12,4,1] => 805 [12,3,2] => 802 [12,3,1,1] => 810 [12,2,2,1] => 810 [12,2,1,1,1] => 825 [12,1,1,1,1,1] => 850 [11,6] => 705 [11,5,1] => 693 [11,4,2] => 685 [11,4,1,1] => 693 [11,3,3] => 681 [11,3,2,1] => 690 [11,3,1,1,1] => 705 [11,2,2,2] => 693 [11,2,2,1,1] => 705 [11,2,1,1,1,1] => 729 [11,1,1,1,1,1,1] => 765 [10,7] => 630 [10,6,1] => 609 [10,5,2] => 594 [10,5,1,1] => 602 [10,4,3] => 585 [10,4,2,1] => 594 [10,4,1,1,1] => 609 [10,3,3,1] => 590 [10,3,2,2] => 594 [10,3,2,1,1] => 606 [10,3,1,1,1,1] => 630 [10,2,2,2,1] => 609 [10,2,2,1,1,1] => 630 [10,2,1,1,1,1,1] => 665 [10,1,1,1,1,1,1,1] => 714 [9,8] => 585 [9,7,1] => 553 [9,6,2] => 529 [9,6,1,1] => 537 [9,5,3] => 513 [9,5,2,1] => 522 [9,5,1,1,1] => 537 [9,4,4] => 505 [9,4,3,1] => 513 [9,4,2,2] => 517 [9,4,2,1,1] => 529 [9,4,1,1,1,1] => 553 [9,3,3,2] => 513 [9,3,3,1,1] => 525 [9,3,2,2,1] => 529 [9,3,2,1,1,1] => 550 [9,3,1,1,1,1,1] => 585 [9,2,2,2,2] => 537 [9,2,2,2,1,1] => 553 [9,2,2,1,1,1,1] => 585 [9,2,1,1,1,1,1,1] => 633 [9,1,1,1,1,1,1,1,1] => 697 [8,8,1] => 525 [8,7,2] => 490 [8,7,1,1] => 498 [8,6,3] => 465 [8,6,2,1] => 474 [8,6,1,1,1] => 489 [8,5,4] => 450 [8,5,3,1] => 458 [8,5,2,2] => 462 [8,5,2,1,1] => 474 [8,5,1,1,1,1] => 498 [8,4,4,1] => 450 [8,4,3,2] => 453 [8,4,3,1,1] => 465 [8,4,2,2,1] => 469 [8,4,2,1,1,1] => 490 [8,4,1,1,1,1,1] => 525 [8,3,3,3] => 450 [8,3,3,2,1] => 465 [8,3,3,1,1,1] => 486 [8,3,2,2,2] => 474 [8,3,2,2,1,1] => 490 [8,3,2,1,1,1,1] => 522 [8,3,1,1,1,1,1,1] => 570 [8,2,2,2,2,1] => 498 [8,2,2,2,1,1,1] => 525 [8,2,2,1,1,1,1,1] => 570 [8,2,1,1,1,1,1,1,1] => 633 [8,1,1,1,1,1,1,1,1,1] => 714 [7,7,3] => 441 [7,7,2,1] => 450 [7,7,1,1,1] => 465 [7,6,4] => 417 [7,6,3,1] => 425 [7,6,2,2] => 429 [7,6,2,1,1] => 441 [7,6,1,1,1,1] => 465 [7,5,5] => 405 [7,5,4,1] => 410 [7,5,3,2] => 413 [7,5,3,1,1] => 425 [7,5,2,2,1] => 429 [7,5,2,1,1,1] => 450 [7,5,1,1,1,1,1] => 485 [7,4,4,2] => 405 [7,4,4,1,1] => 417 [7,4,3,3] => 405 [7,4,3,2,1] => 420 [7,4,3,1,1,1] => 441 [7,4,2,2,2] => 429 [7,4,2,2,1,1] => 445 [7,4,2,1,1,1,1] => 477 [7,4,1,1,1,1,1,1] => 525 [7,3,3,3,1] => 417 [7,3,3,2,2] => 425 [7,3,3,2,1,1] => 441 [7,3,3,1,1,1,1] => 473 [7,3,2,2,2,1] => 450 [7,3,2,2,1,1,1] => 477 [7,3,2,1,1,1,1,1] => 522 [7,3,1,1,1,1,1,1,1] => 585 [7,2,2,2,2,2] => 465 [7,2,2,2,2,1,1] => 485 [7,2,2,2,1,1,1,1] => 525 [7,2,2,1,1,1,1,1,1] => 585 [7,2,1,1,1,1,1,1,1,1] => 665 [7,1,1,1,1,1,1,1,1,1,1] => 765 [6,6,5] => 385 [6,6,4,1] => 390 [6,6,3,2] => 393 [6,6,3,1,1] => 405 [6,6,2,2,1] => 409 [6,6,2,1,1,1] => 430 [6,6,1,1,1,1,1] => 465 [6,5,5,1] => 378 [6,5,4,2] => 378 [6,5,4,1,1] => 390 [6,5,3,3] => 378 [6,5,3,2,1] => 393 [6,5,3,1,1,1] => 414 [6,5,2,2,2] => 402 [6,5,2,2,1,1] => 418 [6,5,2,1,1,1,1] => 450 [6,5,1,1,1,1,1,1] => 498 [6,4,4,3] => 370 [6,4,4,2,1] => 385 [6,4,4,1,1,1] => 406 [6,4,3,3,1] => 385 [6,4,3,2,2] => 393 [6,4,3,2,1,1] => 409 [6,4,3,1,1,1,1] => 441 [6,4,2,2,2,1] => 418 [6,4,2,2,1,1,1] => 445 [6,4,2,1,1,1,1,1] => 490 [6,4,1,1,1,1,1,1,1] => 553 [6,3,3,3,2] => 390 [6,3,3,3,1,1] => 406 [6,3,3,2,2,1] => 414 [6,3,3,2,1,1,1] => 441 [6,3,3,1,1,1,1,1] => 486 [6,3,2,2,2,2] => 430 [6,3,2,2,2,1,1] => 450 [6,3,2,2,1,1,1,1] => 490 [6,3,2,1,1,1,1,1,1] => 550 [6,3,1,1,1,1,1,1,1,1] => 630 [6,2,2,2,2,2,1] => 465 [6,2,2,2,2,1,1,1] => 498 [6,2,2,2,1,1,1,1,1] => 553 [6,2,2,1,1,1,1,1,1,1] => 630 [6,2,1,1,1,1,1,1,1,1,1] => 729 [6,1,1,1,1,1,1,1,1,1,1,1] => 850 [5,5,5,2] => 357 [5,5,5,1,1] => 369 [5,5,4,3] => 354 [5,5,4,2,1] => 369 [5,5,4,1,1,1] => 390 [5,5,3,3,1] => 369 [5,5,3,2,2] => 377 [5,5,3,2,1,1] => 393 [5,5,3,1,1,1,1] => 425 [5,5,2,2,2,1] => 402 [5,5,2,2,1,1,1] => 429 [5,5,2,1,1,1,1,1] => 474 [5,5,1,1,1,1,1,1,1] => 537 [5,4,4,4] => 345 [5,4,4,3,1] => 361 [5,4,4,2,2] => 369 [5,4,4,2,1,1] => 385 [5,4,4,1,1,1,1] => 417 [5,4,3,3,2] => 369 [5,4,3,3,1,1] => 385 [5,4,3,2,2,1] => 393 [5,4,3,2,1,1,1] => 420 [5,4,3,1,1,1,1,1] => 465 [5,4,2,2,2,2] => 409 [5,4,2,2,2,1,1] => 429 [5,4,2,2,1,1,1,1] => 469 [5,4,2,1,1,1,1,1,1] => 529 [5,4,1,1,1,1,1,1,1,1] => 609 [5,3,3,3,3] => 369 [5,3,3,3,2,1] => 390 [5,3,3,3,1,1,1] => 417 [5,3,3,2,2,2] => 405 [5,3,3,2,2,1,1] => 425 [5,3,3,2,1,1,1,1] => 465 [5,3,3,1,1,1,1,1,1] => 525 [5,3,2,2,2,2,1] => 441 [5,3,2,2,2,1,1,1] => 474 [5,3,2,2,1,1,1,1,1] => 529 [5,3,2,1,1,1,1,1,1,1] => 606 [5,3,1,1,1,1,1,1,1,1,1] => 705 [5,2,2,2,2,2,2] => 465 [5,2,2,2,2,2,1,1] => 489 [5,2,2,2,2,1,1,1,1] => 537 [5,2,2,2,1,1,1,1,1,1] => 609 [5,2,2,1,1,1,1,1,1,1,1] => 705 [5,2,1,1,1,1,1,1,1,1,1,1] => 825 [5,1,1,1,1,1,1,1,1,1,1,1,1] => 969 [4,4,4,4,1] => 345 [4,4,4,3,2] => 354 [4,4,4,3,1,1] => 370 [4,4,4,2,2,1] => 378 [4,4,4,2,1,1,1] => 405 [4,4,4,1,1,1,1,1] => 450 [4,4,3,3,3] => 357 [4,4,3,3,2,1] => 378 [4,4,3,3,1,1,1] => 405 [4,4,3,2,2,2] => 393 [4,4,3,2,2,1,1] => 413 [4,4,3,2,1,1,1,1] => 453 [4,4,3,1,1,1,1,1,1] => 513 [4,4,2,2,2,2,1] => 429 [4,4,2,2,2,1,1,1] => 462 [4,4,2,2,1,1,1,1,1] => 517 [4,4,2,1,1,1,1,1,1,1] => 594 [4,4,1,1,1,1,1,1,1,1,1] => 693 [4,3,3,3,3,1] => 378 [4,3,3,3,2,2] => 390 [4,3,3,3,2,1,1] => 410 [4,3,3,3,1,1,1,1] => 450 [4,3,3,2,2,2,1] => 425 [4,3,3,2,2,1,1,1] => 458 [4,3,3,2,1,1,1,1,1] => 513 [4,3,3,1,1,1,1,1,1,1] => 590 [4,3,2,2,2,2,2] => 450 [4,3,2,2,2,2,1,1] => 474 [4,3,2,2,2,1,1,1,1] => 522 [4,3,2,2,1,1,1,1,1,1] => 594 [4,3,2,1,1,1,1,1,1,1,1] => 690 [4,3,1,1,1,1,1,1,1,1,1,1] => 810 [4,2,2,2,2,2,2,1] => 498 [4,2,2,2,2,2,1,1,1] => 537 [4,2,2,2,2,1,1,1,1,1] => 602 [4,2,2,2,1,1,1,1,1,1,1] => 693 [4,2,2,1,1,1,1,1,1,1,1,1] => 810 [4,2,1,1,1,1,1,1,1,1,1,1,1] => 953 [4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1122 [3,3,3,3,3,2] => 385 [3,3,3,3,3,1,1] => 405 [3,3,3,3,2,2,1] => 417 [3,3,3,3,2,1,1,1] => 450 [3,3,3,3,1,1,1,1,1] => 505 [3,3,3,2,2,2,2] => 441 [3,3,3,2,2,2,1,1] => 465 [3,3,3,2,2,1,1,1,1] => 513 [3,3,3,2,1,1,1,1,1,1] => 585 [3,3,3,1,1,1,1,1,1,1,1] => 681 [3,3,2,2,2,2,2,1] => 490 [3,3,2,2,2,2,1,1,1] => 529 [3,3,2,2,2,1,1,1,1,1] => 594 [3,3,2,2,1,1,1,1,1,1,1] => 685 [3,3,2,1,1,1,1,1,1,1,1,1] => 802 [3,3,1,1,1,1,1,1,1,1,1,1,1] => 945 [3,2,2,2,2,2,2,2] => 525 [3,2,2,2,2,2,2,1,1] => 553 [3,2,2,2,2,2,1,1,1,1] => 609 [3,2,2,2,2,1,1,1,1,1,1] => 693 [3,2,2,2,1,1,1,1,1,1,1,1] => 805 [3,2,2,1,1,1,1,1,1,1,1,1,1] => 945 ----------------------------------------------------------------------------- Created: Mar 11, 2024 at 11:27 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Mar 11, 2024 at 11:27 by Martin Rubey