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Identifier
Values
=>
Cc0002;cc-rep
[]=>0 [1]=>1 [2]=>3 [1,1]=>3 [3]=>6 [2,1]=>5 [1,1,1]=>6 [4]=>10 [3,1]=>8 [2,2]=>8 [2,1,1]=>8 [1,1,1,1]=>10 [5]=>15 [4,1]=>12 [3,2]=>11 [3,1,1]=>11 [2,2,1]=>11 [2,1,1,1]=>12 [1,1,1,1,1]=>15 [6]=>21 [5,1]=>17 [4,2]=>15 [4,1,1]=>15 [3,3]=>15 [3,2,1]=>14 [3,1,1,1]=>15 [2,2,2]=>15 [2,2,1,1]=>15 [2,1,1,1,1]=>17 [1,1,1,1,1,1]=>21 [7]=>28 [6,1]=>23 [5,2]=>20 [5,1,1]=>20 [4,3]=>19 [4,2,1]=>18 [4,1,1,1]=>19 [3,3,1]=>18 [3,2,2]=>18 [3,2,1,1]=>18 [3,1,1,1,1]=>20 [2,2,2,1]=>19 [2,2,1,1,1]=>20 [2,1,1,1,1,1]=>23 [1,1,1,1,1,1,1]=>28 [8]=>36 [7,1]=>30 [6,2]=>26 [6,1,1]=>26 [5,3]=>24 [5,2,1]=>23 [5,1,1,1]=>24 [4,4]=>24 [4,3,1]=>22 [4,2,2]=>22 [4,2,1,1]=>22 [4,1,1,1,1]=>24 [3,3,2]=>22 [3,3,1,1]=>22 [3,2,2,1]=>22 [3,2,1,1,1]=>23 [3,1,1,1,1,1]=>26 [2,2,2,2]=>24 [2,2,2,1,1]=>24 [2,2,1,1,1,1]=>26 [2,1,1,1,1,1,1]=>30 [1,1,1,1,1,1,1,1]=>36 [9]=>45 [8,1]=>38 [7,2]=>33 [7,1,1]=>33 [6,3]=>30 [6,2,1]=>29 [6,1,1,1]=>30 [5,4]=>29 [5,3,1]=>27 [5,2,2]=>27 [5,2,1,1]=>27 [5,1,1,1,1]=>29 [4,4,1]=>27 [4,3,2]=>26 [4,3,1,1]=>26 [4,2,2,1]=>26 [4,2,1,1,1]=>27 [4,1,1,1,1,1]=>30 [3,3,3]=>27 [3,3,2,1]=>26 [3,3,1,1,1]=>27 [3,2,2,2]=>27 [3,2,2,1,1]=>27 [3,2,1,1,1,1]=>29 [3,1,1,1,1,1,1]=>33 [2,2,2,2,1]=>29 [2,2,2,1,1,1]=>30 [2,2,1,1,1,1,1]=>33 [2,1,1,1,1,1,1,1]=>38 [1,1,1,1,1,1,1,1,1]=>45 [10]=>55 [9,1]=>47 [8,2]=>41 [8,1,1]=>41 [7,3]=>37 [7,2,1]=>36 [7,1,1,1]=>37 [6,4]=>35 [6,3,1]=>33 [6,2,2]=>33 [6,2,1,1]=>33 [6,1,1,1,1]=>35 [5,5]=>35 [5,4,1]=>32 [5,3,2]=>31 [5,3,1,1]=>31 [5,2,2,1]=>31 [5,2,1,1,1]=>32 [5,1,1,1,1,1]=>35 [4,4,2]=>31 [4,4,1,1]=>31 [4,3,3]=>31 [4,3,2,1]=>30 [4,3,1,1,1]=>31 [4,2,2,2]=>31 [4,2,2,1,1]=>31 [4,2,1,1,1,1]=>33 [4,1,1,1,1,1,1]=>37 [3,3,3,1]=>31 [3,3,2,2]=>31 [3,3,2,1,1]=>31 [3,3,1,1,1,1]=>33 [3,2,2,2,1]=>32 [3,2,2,1,1,1]=>33 [3,2,1,1,1,1,1]=>36 [3,1,1,1,1,1,1,1]=>41 [2,2,2,2,2]=>35 [2,2,2,2,1,1]=>35 [2,2,2,1,1,1,1]=>37 [2,2,1,1,1,1,1,1]=>41 [2,1,1,1,1,1,1,1,1]=>47 [1,1,1,1,1,1,1,1,1,1]=>55 [11]=>66 [10,1]=>57 [9,2]=>50 [9,1,1]=>50 [8,3]=>45 [8,2,1]=>44 [8,1,1,1]=>45 [7,4]=>42 [7,3,1]=>40 [7,2,2]=>40 [7,2,1,1]=>40 [7,1,1,1,1]=>42 [6,5]=>41 [6,4,1]=>38 [6,3,2]=>37 [6,3,1,1]=>37 [6,2,2,1]=>37 [6,2,1,1,1]=>38 [6,1,1,1,1,1]=>41 [5,5,1]=>38 [5,4,2]=>36 [5,4,1,1]=>36 [5,3,3]=>36 [5,3,2,1]=>35 [5,3,1,1,1]=>36 [5,2,2,2]=>36 [5,2,2,1,1]=>36 [5,2,1,1,1,1]=>38 [5,1,1,1,1,1,1]=>42 [4,4,3]=>36 [4,4,2,1]=>35 [4,4,1,1,1]=>36 [4,3,3,1]=>35 [4,3,2,2]=>35 [4,3,2,1,1]=>35 [4,3,1,1,1,1]=>37 [4,2,2,2,1]=>36 [4,2,2,1,1,1]=>37 [4,2,1,1,1,1,1]=>40 [4,1,1,1,1,1,1,1]=>45 [3,3,3,2]=>36 [3,3,3,1,1]=>36 [3,3,2,2,1]=>36 [3,3,2,1,1,1]=>37 [3,3,1,1,1,1,1]=>40 [3,2,2,2,2]=>38 [3,2,2,2,1,1]=>38 [3,2,2,1,1,1,1]=>40 [3,2,1,1,1,1,1,1]=>44 [3,1,1,1,1,1,1,1,1]=>50 [2,2,2,2,2,1]=>41 [2,2,2,2,1,1,1]=>42 [2,2,2,1,1,1,1,1]=>45 [2,2,1,1,1,1,1,1,1]=>50 [2,1,1,1,1,1,1,1,1,1]=>57 [1,1,1,1,1,1,1,1,1,1,1]=>66 [12]=>78 [11,1]=>68 [10,2]=>60 [10,1,1]=>60 [9,3]=>54 [9,2,1]=>53 [9,1,1,1]=>54 [8,4]=>50 [8,3,1]=>48 [8,2,2]=>48 [8,2,1,1]=>48 [8,1,1,1,1]=>50 [7,5]=>48 [7,4,1]=>45 [7,3,2]=>44 [7,3,1,1]=>44 [7,2,2,1]=>44 [7,2,1,1,1]=>45 [7,1,1,1,1,1]=>48 [6,6]=>48 [6,5,1]=>44 [6,4,2]=>42 [6,4,1,1]=>42 [6,3,3]=>42 [6,3,2,1]=>41 [6,3,1,1,1]=>42 [6,2,2,2]=>42 [6,2,2,1,1]=>42 [6,2,1,1,1,1]=>44 [6,1,1,1,1,1,1]=>48 [5,5,2]=>42 [5,5,1,1]=>42 [5,4,3]=>41 [5,4,2,1]=>40 [5,4,1,1,1]=>41 [5,3,3,1]=>40 [5,3,2,2]=>40 [5,3,2,1,1]=>40 [5,3,1,1,1,1]=>42 [5,2,2,2,1]=>41 [5,2,2,1,1,1]=>42 [5,2,1,1,1,1,1]=>45 [5,1,1,1,1,1,1,1]=>50 [4,4,4]=>42 [4,4,3,1]=>40 [4,4,2,2]=>40 [4,4,2,1,1]=>40 [4,4,1,1,1,1]=>42 [4,3,3,2]=>40 [4,3,3,1,1]=>40 [4,3,2,2,1]=>40 [4,3,2,1,1,1]=>41 [4,3,1,1,1,1,1]=>44 [4,2,2,2,2]=>42 [4,2,2,2,1,1]=>42 [4,2,2,1,1,1,1]=>44 [4,2,1,1,1,1,1,1]=>48 [4,1,1,1,1,1,1,1,1]=>54 [3,3,3,3]=>42 [3,3,3,2,1]=>41 [3,3,3,1,1,1]=>42 [3,3,2,2,2]=>42 [3,3,2,2,1,1]=>42 [3,3,2,1,1,1,1]=>44 [3,3,1,1,1,1,1,1]=>48 [3,2,2,2,2,1]=>44 [3,2,2,2,1,1,1]=>45 [3,2,2,1,1,1,1,1]=>48 [3,2,1,1,1,1,1,1,1]=>53 [3,1,1,1,1,1,1,1,1,1]=>60 [2,2,2,2,2,2]=>48 [2,2,2,2,2,1,1]=>48 [2,2,2,2,1,1,1,1]=>50 [2,2,2,1,1,1,1,1,1]=>54 [2,2,1,1,1,1,1,1,1,1]=>60 [2,1,1,1,1,1,1,1,1,1,1]=>68 [1,1,1,1,1,1,1,1,1,1,1,1]=>78 [13]=>91 [12,1]=>80 [10,3]=>64 [9,4]=>59 [9,2,2]=>57 [8,5]=>56 [8,4,1]=>53 [8,3,2]=>52 [8,3,1,1]=>52 [7,6]=>55 [7,5,1]=>51 [7,4,2]=>49 [7,4,1,1]=>49 [7,3,3]=>49 [7,3,2,1]=>48 [6,6,1]=>51 [6,5,2]=>48 [6,5,1,1]=>48 [6,4,3]=>47 [6,4,2,1]=>46 [6,3,3,1]=>46 [6,3,2,2]=>46 [6,3,1,1,1,1]=>48 [6,2,2,1,1,1]=>48 [6,1,1,1,1,1,1,1]=>56 [5,5,3]=>47 [5,5,2,1]=>46 [5,4,4]=>47 [5,4,3,1]=>45 [5,4,2,2]=>45 [5,4,2,1,1]=>45 [5,4,1,1,1,1]=>47 [5,3,3,2]=>45 [5,3,3,1,1]=>45 [5,3,2,2,1]=>45 [5,3,2,1,1,1]=>46 [5,3,1,1,1,1,1]=>49 [5,2,2,2,1,1]=>47 [5,2,2,1,1,1,1]=>49 [5,2,1,1,1,1,1,1]=>53 [4,4,4,1]=>46 [4,4,3,2]=>45 [4,4,3,1,1]=>45 [4,4,2,2,1]=>45 [4,3,3,3]=>46 [4,3,3,2,1]=>45 [3,3,3,3,1]=>47 [3,3,3,2,2]=>47 [3,3,3,2,1,1]=>47 [3,3,2,2,2,1]=>48 [3,3,2,2,1,1,1]=>49 [3,3,2,1,1,1,1,1]=>52 [3,2,2,2,2,2]=>51 [3,2,2,2,2,1,1]=>51 [3,1,1,1,1,1,1,1,1,1,1]=>71 [2,2,2,2,2,2,1]=>55 [2,2,2,2,1,1,1,1,1]=>59 [1,1,1,1,1,1,1,1,1,1,1,1,1]=>91 [14]=>105 [13,1]=>93 [12,2]=>83 [12,1,1]=>83 [11,2,1]=>74 [10,2,2]=>67 [9,5]=>65 [8,6]=>63 [8,5,1]=>59 [8,4,2]=>57 [8,3,3]=>57 [8,3,1,1,1]=>57 [7,7]=>63 [7,6,1]=>58 [7,5,2]=>55 [7,4,3]=>54 [6,6,2]=>55 [6,6,1,1]=>55 [6,5,3]=>53 [6,5,1,1,1]=>53 [6,4,4]=>53 [6,4,2,2]=>51 [6,2,2,2,2]=>53 [6,1,1,1,1,1,1,1,1]=>65 [5,5,4]=>53 [5,5,1,1,1,1]=>53 [5,4,4,1]=>51 [5,4,3,2]=>50 [5,4,3,1,1]=>50 [5,4,2,2,1]=>50 [5,4,2,1,1,1]=>51 [5,4,1,1,1,1,1]=>54 [5,3,3,3]=>51 [5,3,3,2,1]=>50 [5,3,2,2,2]=>51 [5,3,2,2,1,1]=>51 [5,3,2,1,1,1,1]=>53 [5,3,1,1,1,1,1,1]=>57 [5,2,2,2,2,1]=>53 [5,2,2,1,1,1,1,1]=>57 [4,4,4,2]=>51 [4,4,4,1,1]=>51 [4,4,3,3]=>51 [4,4,3,2,1]=>50 [4,3,2,2,2,1]=>52 [3,3,3,3,2]=>53 [3,3,3,3,1,1]=>53 [3,3,3,2,2,1]=>53 [3,3,2,2,2,2]=>55 [3,3,1,1,1,1,1,1,1,1]=>67 [3,2,2,2,2,1,1,1]=>59 [2,2,2,2,2,2,2]=>63 [1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>105 [15]=>120 [14,1]=>107 [12,3]=>87 [11,2,2]=>78 [9,6]=>72 [9,5,1]=>68 [9,3,2,1]=>65 [8,7]=>71 [8,5,2]=>63 [7,5,3]=>60 [6,6,3]=>60 [6,5,4]=>59 [6,5,1,1,1,1]=>59 [6,4,3,1,1]=>56 [6,3,3,3]=>57 [6,3,1,1,1,1,1,1]=>63 [6,2,2,2,2,1]=>59 [5,5,5]=>60 [5,5,2,2,1]=>56 [5,4,3,3]=>56 [5,4,3,2,1]=>55 [5,4,3,1,1,1]=>56 [5,3,2,2,2,1]=>57 [5,3,2,2,1,1,1]=>58 [5,3,1,1,1,1,1,1,1]=>66 [4,4,4,3]=>57 [4,4,4,1,1,1]=>57 [4,3,3,3,2]=>57 [3,3,3,3,3]=>60 [3,3,3,3,2,1]=>59 [3,3,3,2,2,2]=>60 [2,2,2,2,2,2,2,1]=>71 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>120 [16]=>136 [15,1]=>122 [12,4]=>92 [12,1,1,1,1]=>92 [10,6]=>82 [8,8]=>80 [8,6,2]=>70 [8,5,3]=>68 [7,6,3]=>67 [7,5,3,1]=>64 [7,3,3,2,1]=>63 [6,6,4]=>66 [6,6,2,2]=>64 [6,5,5]=>66 [6,4,3,3]=>62 [5,5,3,3]=>62 [5,5,2,2,2]=>62 [5,4,4,3]=>62 [5,4,3,2,1,1]=>61 [5,4,2,2,2,1]=>62 [4,4,4,4]=>64 [4,4,4,2,2]=>62 [4,4,3,3,2]=>62 [4,4,2,2,2,2]=>64 [4,3,3,3,3]=>64 [4,3,3,3,2,1]=>63 [3,3,3,3,2,2]=>66 [3,3,3,3,1,1,1,1]=>68 [3,3,2,2,2,2,2]=>70 [2,2,2,2,2,2,2,2]=>80 [2,2,2,2,2,2,1,1,1,1]=>82 [2,2,2,2,1,1,1,1,1,1,1,1]=>92 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>136 [17]=>153 [16,1]=>138 [9,8]=>89 [8,8,1]=>83 [8,6,3]=>75 [7,5,3,2]=>69 [6,5,3,3]=>68 [6,5,2,2,2]=>68 [6,4,4,3]=>68 [6,4,4,1,1,1]=>68 [6,3,3,3,2]=>68 [6,3,3,3,1,1]=>68 [5,5,4,3]=>68 [5,5,4,1,1,1]=>68 [5,5,2,2,2,1]=>68 [5,4,4,4]=>69 [5,4,3,2,2,1]=>67 [5,3,3,3,2,1]=>68 [4,4,4,3,2]=>68 [4,4,4,3,1,1]=>68 [4,4,4,2,2,1]=>68 [4,4,3,3,3]=>69 [3,3,3,3,3,2]=>73 [3,2,2,2,2,2,2,2]=>83 [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>125 [4,4,4,3,2,1]=>74 [5,4,3,3,2,1]=>73 [6,3,3,3,2,1]=>74 [6,5,2,2,2,1]=>74 [5,5,3,3,1,1]=>73 [6,5,4,1,1,1]=>74 [5,5,3,3,2]=>73 [5,5,4,2,2]=>73 [6,4,4,2,2]=>73 [6,5,4,3]=>74 [4,4,4,3,3]=>75 [4,4,4,4,2]=>75 [5,5,4,4]=>75 [6,4,4,4]=>75 [2,2,2,2,2,2,2,2,2]=>99 [3,3,3,3,3,3]=>81 [18]=>171 [6,2,2,2,2,2,2]=>81 [6,6,6]=>81 [4,2,2,2,2,2,2,2]=>87 [10,4,4]=>87 [9,6,3]=>84 [8,6,4]=>81 [10,8]=>99 [3,3,3,3,1,1,1,1,1,1]=>87 [9,9]=>99 [7,7,1,1,1,1]=>81 [5,4,4,3,2,1]=>79 [5,5,3,3,2,1]=>79 [5,5,4,2,2,1]=>79 [6,4,4,2,2,1]=>79 [5,5,4,3,1,1]=>79 [6,4,4,3,1,1]=>79 [6,5,3,3,1,1]=>79 [5,5,4,3,2]=>79 [6,4,4,3,2]=>79 [6,5,3,3,2]=>79 [6,5,4,2,2]=>79 [6,5,4,3,1]=>79 [6,5,4,1,1,1,1]=>81 [4,4,4,4,3]=>82 [4,3,3,3,3,3]=>85 [19]=>190 [7,2,2,2,2,2,2]=>88 [7,6,6]=>88 [5,2,2,2,2,2,2,2]=>92 [13,6]=>118 [11,4,4]=>98 [9,6,4]=>90 [8,5,4,2]=>83 [8,5,5,1]=>85 [5,5,4,3,2,1]=>85 [6,4,4,3,2,1]=>85 [6,5,3,3,2,1]=>85 [6,5,4,2,2,1]=>85 [6,5,4,3,1,1]=>85 [6,5,4,3,2]=>85 [6,5,2,2,2,2,1]=>88 [6,5,4,2,1,1,1]=>86 [6,6,2,2,2,2]=>88 [7,5,4,3,1]=>86 [2,2,2,2,2,2,2,2,2,2]=>120 [3,3,3,3,3,3,2]=>96 [4,4,3,3,3,3]=>90 [4,4,4,4,4]=>90 [5,5,5,5]=>90 [20]=>210 [10,10]=>120 [8,2,2,2,2,2,2]=>96 [8,6,4,2]=>90 [8,6,6]=>96 [10,6,4]=>100 [9,8,3]=>101 [6,6,6,2]=>90 [10,7,3]=>102 [9,7,4]=>98 [9,5,5,1]=>94 [6,5,4,3,2,1]=>91 [6,3,3,3,3,2,1]=>95 [6,5,3,2,2,2,1]=>93 [6,5,4,3,1,1,1]=>92 [7,6,2,2,2,2]=>95 [6,6,5,4]=>95 [3,3,3,3,3,3,3]=>105 [4,4,4,3,3,3]=>96 [21]=>231 [11,7,3]=>113 [5,4,2,2,2,2,2,2]=>101 [11,10]=>131 [13,4,4]=>123 [7,6,6,2]=>97 [4,4,4,4,3,2,1]=>102 [6,4,3,3,3,2,1]=>100 [6,5,4,2,2,2,1]=>99 [6,5,4,3,2,1,1]=>98 [4,4,4,4,3,3]=>103 [8,6,2,2,2,2]=>103 [22]=>253 [9,6,4,3]=>105 [8,7,7]=>113 [5,4,4,4,3,2,1]=>107 [6,5,3,3,3,2,1]=>106 [6,5,4,3,2,2,1]=>105 [15,2,2,2,2]=>152 [9,6,5,3]=>112 [8,6,5,3,1]=>108 [6,4,4,4,3,2,1]=>113 [6,5,4,3,3,2,1]=>112 [3,3,3,3,3,3,3,3]=>132 [4,4,4,4,4,4]=>120 [6,6,6,6]=>120 [24]=>300 [11,7,5,1]=>130 [9,7,5,3]=>120 [8,8,8]=>132 [17,7]=>188 [12,9,3]=>144 [5,5,5,4,3,2,1]=>120 [6,5,4,4,3,2,1]=>119 [7,6,6,6]=>127 [5,4,4,4,2,2,2,2]=>125 [13,12]=>181 [15,5,5]=>165 [9,7,5,3,1]=>125 [10,7,5,3]=>130 [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1]=>165 [5,5,5,5,5]=>125 [12,10,3]=>155 [6,5,5,4,3,2,1]=>126 [6,6,4,3,3,2,2]=>127 [8,6,6,6]=>135 [9,7,5,4,1]=>132 [16,8,2]=>187 [6,6,5,4,3,2,1]=>133 [7,6,5,4,3,2]=>133 [3,3,3,3,3,3,3,3,3]=>162 [15,6,6]=>180 [7,6,5,4,3,2,1]=>140 [6,6,6,4,3,3]=>142 [4,3,3,3,3,3,3,3,3]=>166 [7,6,5,4,3,1,1,1]=>141 [10,7,6,4,1]=>150 [9,7,6,4,2]=>146 [10,8,5,4,1]=>151 [15,14]=>239 [7,6,5,4,3,2,1,1]=>148 [7,6,5,4,2,2,2,1]=>149 [10,8,6,4,1]=>159 [6,6,6,6,6]=>165 [15,15]=>255 [5,5,5,5,5,5]=>165 [6,6,6,6,3,3]=>159 [10,10,10]=>195 [9,7,5,5,3,1]=>159 [7,6,5,4,3,2,2,1]=>156 [7,6,5,3,3,3,2,1]=>157 [11,8,6,4,1]=>170 [10,8,6,4,2]=>165 [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>255 [7,6,6,6,6]=>172 [7,6,5,4,3,3,2,1]=>164 [7,6,4,4,4,3,2,1]=>165 [11,8,6,5,1]=>178 [10,10,9,2]=>192 [14,9,8]=>211 [4,4,4,4,4,4,4,4]=>192 [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>288 [7,6,5,4,4,3,2,1]=>172 [7,5,5,5,4,3,2,1]=>173 [16,16]=>288 [10,10,10,2]=>204 [16,8,4,2,2]=>218 [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>291 [5,4,4,4,4,4,4,4]=>197 [7,6,5,5,4,3,2,1]=>180 [6,6,6,5,4,3,2,1]=>181 [22,7,4]=>306 [12,12,4,3,2]=>212 [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>295 [7,6,6,5,4,3,2,1]=>188 [12,9,7,5,1]=>209 [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>280 [7,7,6,5,4,3,2,1]=>196 [13,9,7,5,1]=>222 [18,18]=>360 [24,12]=>390 [11,9,7,5,3,1]=>216 [11,8,7,5,4,1]=>214 [8,7,6,5,4,3,2,1]=>204 [8,7,7,7,7]=>218 [7,6,2,2,2,2,2,2,2,2,2,2,2,2]=>271 [7,6,6,6,6,6]=>223 [8,7,6,5,4,3,2,1,1]=>213 [8,7,6,5,4,3,2,2,1]=>222 [8,7,6,5,4,3,3,2,1]=>231 [10,10,10,10]=>280 [12,12,12,4]=>292 [8,7,6,5,4,4,3,2,1]=>240 [11,9,7,5,5,3]=>248 [4,4,4,4,4,4,4,4,4,4]=>280 [14,14,8,4]=>298 [7,6,6,6,2,2,2,2,2,2,2,2]=>271 [8,7,6,5,5,4,3,2,1]=>249 [9,9,9,9,3,3]=>273 [8,7,6,6,5,4,3,2,1]=>258 [10,10,10,5,5,2]=>273 [16,10,8,8]=>313 [26,9,7]=>447 [8,7,7,6,5,4,3,2,1]=>267 [8,8,7,6,5,4,3,2,1]=>276 [18,18,9]=>423 [9,8,7,6,5,4,3,2,1]=>285 [11,9,7,7,5,3,3]=>291 [48]=>1176 [7,6,6,6,6,6,6,6]=>343 [22,9,8,5,5]=>424 [6,6,6,6,6,6,6,3,3,2]=>351 [27,14,9]=>560 [17,14,13,8]=>449 [5,5,5,5,5,5,5,5,5,5,5]=>440 [27,20,8]=>660 [26,13,7,7,2]=>557 [31,12,10,4]=>683 [6,6,6,6,6,6,6,6,6,6]=>480 [5,5,5,5,5,5,5,5,5,5,5,5]=>510 [12,12,12,12,12]=>510 [12,12,12,12,11,4]=>524 [12,12,12,12,12,4]=>540 [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]=>1091 [11,11,11,11,11,10]=>545 [11,11,11,11,11,11]=>561 [16,14,9,9,9,9]=>561 [8,8,8,8,8,8,8,8,4,2]=>575 [24,24,24]=>972 [16,16,16,16,8,4,2]=>753 [12,12,12,12,12,12,4,4]=>720 [22,20,20,12,8]=>915 [20,20,8,4,4,4,4,4,4,4,4,4]=>834 [33,32,9,9,5]=>1291 [18,18,18,18,18]=>1035 [18,18,18,18,9,9]=>963 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3]=>939 [56,17,11,10,5]=>1974 [33,26,23,12,9]=>1455 [22,22,22,10,10,9,4,4]=>1167 [22,22,22,10,10,10,4,4]=>1182 [12,12,12,12,12,12,12,12,4,3,2]=>1058 [24,24,24,24,14]=>1505 [76,22,9,6]=>3303 [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>1610 [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]=>1740 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>1560 [12,12,12,12,12,12,12,12,12,12]=>1320 [24,24,24,24,24]=>1740 [12,12,12,12,12,12,12,12,12,6,6,6,4,2]=>1464 [54,48,18,10,8]=>3069 [24,24,24,24,24,24]=>2160 [37,33,20,20,13,10,10,10,7]=>2389 [42,34,30,22,22,14,2]=>2907 [54,52,34,18,11,7]=>3976 [65,27,27,25,13,9,6,6]=>3735 [18,18,18,18,18,18,18,18,18,18]=>2520 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>3240 [16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2]=>2353 [58,38,38,38,30]=>4747 [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]=>3840 [10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2]=>4428 [74,58,34,34,22,22,13,11,2]=>6939 [61,48,48,48,45,22,12,2]=>7452 [15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3]=>4805 [98,62,36,26,14,14,14,14,14,14,12,2]=>9432 [14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,13,2]=>6840 [14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2]=>6878 [74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3]=>9034 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>11880 [64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6]=>8569 [70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3]=>9347 [14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2]=>9491 [170,92,36,28,27,24,20,14,13,10,8,8]=>22152 [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3]=>11607 [145,83,62,44,44,42,19,16,16,10,8]=>20709 [98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8]=>18090 [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]=>45360
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Description
The sum 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. This statistic is the sum of all hook lengths of a partition.
References
[1] Amdeberhan, T. Average on sum of hooks in a rectangle MathOverflow:273095
Code
def statistic(L):
    return sum(L.hooks())

Created
Jun 27, 2017 at 09:02 by Christian Stump
Updated
Mar 11, 2024 at 11:26 by Martin Rubey