***************************************************************************** * 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: St000198 ----------------------------------------------------------------------------- Collection: Binary trees ----------------------------------------------------------------------------- Description: A decimal representation of a binary tree as a code word. Code word constructed by mapping a binary tree to its corresponding set of matching parentheses and then replacing every '''''(''''' with a $1$ and every ''''')''''' with a $0$. We then convert the resulting binary code word to a decimal number. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def treeToParenthesis(t): singletonTree = BinaryTree(None) parenthesisRepresentation = '()' if (t ==singletonTree): return None else: if (t[0] == singletonTree and t[1] == singletonTree): return parenthesisRepresentation if (t[0] != singletonTree): parenthesisRepresentation='('+treeToParenthesis(t[0])+')' if (t[1] != singletonTree): parenthesisRepresentation+= treeToParenthesis(t[1]) return parenthesisRepresentation def treeToDecimal(t): parenthesisRepresentation = treeToParenthesis(t) decimalRepresentation = 0 if parenthesisRepresentation == None: return decimalRepresentation length = len(parenthesisRepresentation) for x in range(1,length+1): if parenthesisRepresentation[length-x] == "(": decimalRepresentation += 2**(x-1) return decimalRepresentation def statistic(t): return treeToDecimal(t) ----------------------------------------------------------------------------- Statistic values: . => 0 [.,.] => 2 [.,[.,.]] => 10 [[.,.],.] => 12 [.,[.,[.,.]]] => 42 [.,[[.,.],.]] => 44 [[.,.],[.,.]] => 50 [[.,[.,.]],.] => 52 [[[.,.],.],.] => 56 [.,[.,[.,[.,.]]]] => 170 [.,[.,[[.,.],.]]] => 172 [.,[[.,.],[.,.]]] => 178 [.,[[.,[.,.]],.]] => 180 [.,[[[.,.],.],.]] => 184 [[.,.],[.,[.,.]]] => 202 [[.,.],[[.,.],.]] => 204 [[.,[.,.]],[.,.]] => 210 [[[.,.],.],[.,.]] => 226 [[.,[.,[.,.]]],.] => 212 [[.,[[.,.],.]],.] => 216 [[[.,.],[.,.]],.] => 228 [[[.,[.,.]],.],.] => 232 [[[[.,.],.],.],.] => 240 [.,[.,[.,[.,[.,.]]]]] => 682 [.,[.,[.,[[.,.],.]]]] => 684 [.,[.,[[.,.],[.,.]]]] => 690 [.,[.,[[.,[.,.]],.]]] => 692 [.,[.,[[[.,.],.],.]]] => 696 [.,[[.,.],[.,[.,.]]]] => 714 [.,[[.,.],[[.,.],.]]] => 716 [.,[[.,[.,.]],[.,.]]] => 722 [.,[[[.,.],.],[.,.]]] => 738 [.,[[.,[.,[.,.]]],.]] => 724 [.,[[.,[[.,.],.]],.]] => 728 [.,[[[.,.],[.,.]],.]] => 740 [.,[[[.,[.,.]],.],.]] => 744 [.,[[[[.,.],.],.],.]] => 752 [[.,.],[.,[.,[.,.]]]] => 810 [[.,.],[.,[[.,.],.]]] => 812 [[.,.],[[.,.],[.,.]]] => 818 [[.,.],[[.,[.,.]],.]] => 820 [[.,.],[[[.,.],.],.]] => 824 [[.,[.,.]],[.,[.,.]]] => 842 [[.,[.,.]],[[.,.],.]] => 844 [[[.,.],.],[.,[.,.]]] => 906 [[[.,.],.],[[.,.],.]] => 908 [[.,[.,[.,.]]],[.,.]] => 850 [[.,[[.,.],.]],[.,.]] => 866 [[[.,.],[.,.]],[.,.]] => 914 [[[.,[.,.]],.],[.,.]] => 930 [[[[.,.],.],.],[.,.]] => 962 [[.,[.,[.,[.,.]]]],.] => 852 [[.,[.,[[.,.],.]]],.] => 856 [[.,[[.,.],[.,.]]],.] => 868 [[.,[[.,[.,.]],.]],.] => 872 [[.,[[[.,.],.],.]],.] => 880 [[[.,.],[.,[.,.]]],.] => 916 [[[.,.],[[.,.],.]],.] => 920 [[[.,[.,.]],[.,.]],.] => 932 [[[[.,.],.],[.,.]],.] => 964 [[[.,[.,[.,.]]],.],.] => 936 [[[.,[[.,.],.]],.],.] => 944 [[[[.,.],[.,.]],.],.] => 968 [[[[.,[.,.]],.],.],.] => 976 [[[[[.,.],.],.],.],.] => 992 [.,[.,[.,[.,[.,[.,.]]]]]] => 2730 [.,[.,[.,[.,[[.,.],.]]]]] => 2732 [.,[.,[.,[[.,.],[.,.]]]]] => 2738 [.,[.,[.,[[.,[.,.]],.]]]] => 2740 [.,[.,[.,[[[.,.],.],.]]]] => 2744 [.,[.,[[.,.],[.,[.,.]]]]] => 2762 [.,[.,[[.,.],[[.,.],.]]]] => 2764 [.,[.,[[.,[.,.]],[.,.]]]] => 2770 [.,[.,[[[.,.],.],[.,.]]]] => 2786 [.,[.,[[.,[.,[.,.]]],.]]] => 2772 [.,[.,[[.,[[.,.],.]],.]]] => 2776 [.,[.,[[[.,.],[.,.]],.]]] => 2788 [.,[.,[[[.,[.,.]],.],.]]] => 2792 [.,[.,[[[[.,.],.],.],.]]] => 2800 [.,[[.,.],[.,[.,[.,.]]]]] => 2858 [.,[[.,.],[.,[[.,.],.]]]] => 2860 [.,[[.,.],[[.,.],[.,.]]]] => 2866 [.,[[.,.],[[.,[.,.]],.]]] => 2868 [.,[[.,.],[[[.,.],.],.]]] => 2872 [.,[[.,[.,.]],[.,[.,.]]]] => 2890 [.,[[.,[.,.]],[[.,.],.]]] => 2892 [.,[[[.,.],.],[.,[.,.]]]] => 2954 [.,[[[.,.],.],[[.,.],.]]] => 2956 [.,[[.,[.,[.,.]]],[.,.]]] => 2898 [.,[[.,[[.,.],.]],[.,.]]] => 2914 [.,[[[.,.],[.,.]],[.,.]]] => 2962 [.,[[[.,[.,.]],.],[.,.]]] => 2978 [.,[[[[.,.],.],.],[.,.]]] => 3010 [.,[[.,[.,[.,[.,.]]]],.]] => 2900 [.,[[.,[.,[[.,.],.]]],.]] => 2904 [.,[[.,[[.,.],[.,.]]],.]] => 2916 [.,[[.,[[.,[.,.]],.]],.]] => 2920 [.,[[.,[[[.,.],.],.]],.]] => 2928 [.,[[[.,.],[.,[.,.]]],.]] => 2964 [.,[[[.,.],[[.,.],.]],.]] => 2968 [.,[[[.,[.,.]],[.,.]],.]] => 2980 [.,[[[[.,.],.],[.,.]],.]] => 3012 [.,[[[.,[.,[.,.]]],.],.]] => 2984 [.,[[[.,[[.,.],.]],.],.]] => 2992 [.,[[[[.,.],[.,.]],.],.]] => 3016 [.,[[[[.,[.,.]],.],.],.]] => 3024 [.,[[[[[.,.],.],.],.],.]] => 3040 [[.,.],[.,[.,[.,[.,.]]]]] => 3242 [[.,.],[.,[.,[[.,.],.]]]] => 3244 [[.,.],[.,[[.,.],[.,.]]]] => 3250 [[.,.],[.,[[.,[.,.]],.]]] => 3252 [[.,.],[.,[[[.,.],.],.]]] => 3256 [[.,.],[[.,.],[.,[.,.]]]] => 3274 [[.,.],[[.,.],[[.,.],.]]] => 3276 [[.,.],[[.,[.,.]],[.,.]]] => 3282 [[.,.],[[[.,.],.],[.,.]]] => 3298 [[.,.],[[.,[.,[.,.]]],.]] => 3284 [[.,.],[[.,[[.,.],.]],.]] => 3288 [[.,.],[[[.,.],[.,.]],.]] => 3300 [[.,.],[[[.,[.,.]],.],.]] => 3304 [[.,.],[[[[.,.],.],.],.]] => 3312 [[.,[.,.]],[.,[.,[.,.]]]] => 3370 [[.,[.,.]],[.,[[.,.],.]]] => 3372 [[.,[.,.]],[[.,.],[.,.]]] => 3378 [[.,[.,.]],[[.,[.,.]],.]] => 3380 [[.,[.,.]],[[[.,.],.],.]] => 3384 [[[.,.],.],[.,[.,[.,.]]]] => 3626 [[[.,.],.],[.,[[.,.],.]]] => 3628 [[[.,.],.],[[.,.],[.,.]]] => 3634 [[[.,.],.],[[.,[.,.]],.]] => 3636 [[[.,.],.],[[[.,.],.],.]] => 3640 [[.,[.,[.,.]]],[.,[.,.]]] => 3402 [[.,[.,[.,.]]],[[.,.],.]] => 3404 [[.,[[.,.],.]],[.,[.,.]]] => 3466 [[.,[[.,.],.]],[[.,.],.]] => 3468 [[[.,.],[.,.]],[.,[.,.]]] => 3658 [[[.,.],[.,.]],[[.,.],.]] => 3660 [[[.,[.,.]],.],[.,[.,.]]] => 3722 [[[.,[.,.]],.],[[.,.],.]] => 3724 [[[[.,.],.],.],[.,[.,.]]] => 3850 [[[[.,.],.],.],[[.,.],.]] => 3852 [[.,[.,[.,[.,.]]]],[.,.]] => 3410 [[.,[.,[[.,.],.]]],[.,.]] => 3426 [[.,[[.,.],[.,.]]],[.,.]] => 3474 [[.,[[.,[.,.]],.]],[.,.]] => 3490 [[.,[[[.,.],.],.]],[.,.]] => 3522 [[[.,.],[.,[.,.]]],[.,.]] => 3666 [[[.,.],[[.,.],.]],[.,.]] => 3682 [[[.,[.,.]],[.,.]],[.,.]] => 3730 [[[[.,.],.],[.,.]],[.,.]] => 3858 [[[.,[.,[.,.]]],.],[.,.]] => 3746 [[[.,[[.,.],.]],.],[.,.]] => 3778 [[[[.,.],[.,.]],.],[.,.]] => 3874 [[[[.,[.,.]],.],.],[.,.]] => 3906 [[[[[.,.],.],.],.],[.,.]] => 3970 [[.,[.,[.,[.,[.,.]]]]],.] => 3412 [[.,[.,[.,[[.,.],.]]]],.] => 3416 [[.,[.,[[.,.],[.,.]]]],.] => 3428 [[.,[.,[[.,[.,.]],.]]],.] => 3432 [[.,[.,[[[.,.],.],.]]],.] => 3440 [[.,[[.,.],[.,[.,.]]]],.] => 3476 [[.,[[.,.],[[.,.],.]]],.] => 3480 [[.,[[.,[.,.]],[.,.]]],.] => 3492 [[.,[[[.,.],.],[.,.]]],.] => 3524 [[.,[[.,[.,[.,.]]],.]],.] => 3496 [[.,[[.,[[.,.],.]],.]],.] => 3504 [[.,[[[.,.],[.,.]],.]],.] => 3528 [[.,[[[.,[.,.]],.],.]],.] => 3536 [[.,[[[[.,.],.],.],.]],.] => 3552 [[[.,.],[.,[.,[.,.]]]],.] => 3668 [[[.,.],[.,[[.,.],.]]],.] => 3672 [[[.,.],[[.,.],[.,.]]],.] => 3684 [[[.,.],[[.,[.,.]],.]],.] => 3688 [[[.,.],[[[.,.],.],.]],.] => 3696 [[[.,[.,.]],[.,[.,.]]],.] => 3732 [[[.,[.,.]],[[.,.],.]],.] => 3736 [[[[.,.],.],[.,[.,.]]],.] => 3860 [[[[.,.],.],[[.,.],.]],.] => 3864 [[[.,[.,[.,.]]],[.,.]],.] => 3748 [[[.,[[.,.],.]],[.,.]],.] => 3780 [[[[.,.],[.,.]],[.,.]],.] => 3876 [[[[.,[.,.]],.],[.,.]],.] => 3908 [[[[[.,.],.],.],[.,.]],.] => 3972 [[[.,[.,[.,[.,.]]]],.],.] => 3752 [[[.,[.,[[.,.],.]]],.],.] => 3760 [[[.,[[.,.],[.,.]]],.],.] => 3784 [[[.,[[.,[.,.]],.]],.],.] => 3792 [[[.,[[[.,.],.],.]],.],.] => 3808 [[[[.,.],[.,[.,.]]],.],.] => 3880 [[[[.,.],[[.,.],.]],.],.] => 3888 [[[[.,[.,.]],[.,.]],.],.] => 3912 [[[[[.,.],.],[.,.]],.],.] => 3976 [[[[.,[.,[.,.]]],.],.],.] => 3920 [[[[.,[[.,.],.]],.],.],.] => 3936 [[[[[.,.],[.,.]],.],.],.] => 3984 [[[[[.,[.,.]],.],.],.],.] => 4000 [[[[[[.,.],.],.],.],.],.] => 4032 [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 10922 [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 10924 [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 10930 [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 10932 [.,[.,[.,[.,[[[.,.],.],.]]]]] => 10936 [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 10954 [.,[.,[.,[[.,.],[[.,.],.]]]]] => 10956 [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 10962 [.,[.,[.,[[[.,.],.],[.,.]]]]] => 10978 [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 10964 [.,[.,[.,[[.,[[.,.],.]],.]]]] => 10968 [.,[.,[.,[[[.,.],[.,.]],.]]]] => 10980 [.,[.,[.,[[[.,[.,.]],.],.]]]] => 10984 [.,[.,[.,[[[[.,.],.],.],.]]]] => 10992 [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 11050 [.,[.,[[.,.],[.,[[.,.],.]]]]] => 11052 [.,[.,[[.,.],[[.,.],[.,.]]]]] => 11058 [.,[.,[[.,.],[[.,[.,.]],.]]]] => 11060 [.,[.,[[.,.],[[[.,.],.],.]]]] => 11064 [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 11082 [.,[.,[[.,[.,.]],[[.,.],.]]]] => 11084 [.,[.,[[[.,.],.],[.,[.,.]]]]] => 11146 [.,[.,[[[.,.],.],[[.,.],.]]]] => 11148 [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 11090 [.,[.,[[.,[[.,.],.]],[.,.]]]] => 11106 [.,[.,[[[.,.],[.,.]],[.,.]]]] => 11154 [.,[.,[[[.,[.,.]],.],[.,.]]]] => 11170 [.,[.,[[[[.,.],.],.],[.,.]]]] => 11202 [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 11092 [.,[.,[[.,[.,[[.,.],.]]],.]]] => 11096 [.,[.,[[.,[[.,.],[.,.]]],.]]] => 11108 [.,[.,[[.,[[.,[.,.]],.]],.]]] => 11112 [.,[.,[[.,[[[.,.],.],.]],.]]] => 11120 [.,[.,[[[.,.],[.,[.,.]]],.]]] => 11156 [.,[.,[[[.,.],[[.,.],.]],.]]] => 11160 [.,[.,[[[.,[.,.]],[.,.]],.]]] => 11172 [.,[.,[[[[.,.],.],[.,.]],.]]] => 11204 [.,[.,[[[.,[.,[.,.]]],.],.]]] => 11176 [.,[.,[[[.,[[.,.],.]],.],.]]] => 11184 [.,[.,[[[[.,.],[.,.]],.],.]]] => 11208 [.,[.,[[[[.,[.,.]],.],.],.]]] => 11216 [.,[.,[[[[[.,.],.],.],.],.]]] => 11232 [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 11434 [.,[[.,.],[.,[.,[[.,.],.]]]]] => 11436 [.,[[.,.],[.,[[.,.],[.,.]]]]] => 11442 [.,[[.,.],[.,[[.,[.,.]],.]]]] => 11444 [.,[[.,.],[.,[[[.,.],.],.]]]] => 11448 [.,[[.,.],[[.,.],[.,[.,.]]]]] => 11466 [.,[[.,.],[[.,.],[[.,.],.]]]] => 11468 [.,[[.,.],[[.,[.,.]],[.,.]]]] => 11474 [.,[[.,.],[[[.,.],.],[.,.]]]] => 11490 [.,[[.,.],[[.,[.,[.,.]]],.]]] => 11476 [.,[[.,.],[[.,[[.,.],.]],.]]] => 11480 [.,[[.,.],[[[.,.],[.,.]],.]]] => 11492 [.,[[.,.],[[[.,[.,.]],.],.]]] => 11496 [.,[[.,.],[[[[.,.],.],.],.]]] => 11504 [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 11562 [.,[[.,[.,.]],[.,[[.,.],.]]]] => 11564 [.,[[.,[.,.]],[[.,.],[.,.]]]] => 11570 [.,[[.,[.,.]],[[.,[.,.]],.]]] => 11572 [.,[[.,[.,.]],[[[.,.],.],.]]] => 11576 [.,[[[.,.],.],[.,[.,[.,.]]]]] => 11818 [.,[[[.,.],.],[.,[[.,.],.]]]] => 11820 [.,[[[.,.],.],[[.,.],[.,.]]]] => 11826 [.,[[[.,.],.],[[.,[.,.]],.]]] => 11828 [.,[[[.,.],.],[[[.,.],.],.]]] => 11832 [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 11594 [.,[[.,[.,[.,.]]],[[.,.],.]]] => 11596 [.,[[.,[[.,.],.]],[.,[.,.]]]] => 11658 [.,[[.,[[.,.],.]],[[.,.],.]]] => 11660 [.,[[[.,.],[.,.]],[.,[.,.]]]] => 11850 [.,[[[.,.],[.,.]],[[.,.],.]]] => 11852 [.,[[[.,[.,.]],.],[.,[.,.]]]] => 11914 [.,[[[.,[.,.]],.],[[.,.],.]]] => 11916 [.,[[[[.,.],.],.],[.,[.,.]]]] => 12042 [.,[[[[.,.],.],.],[[.,.],.]]] => 12044 [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 11602 [.,[[.,[.,[[.,.],.]]],[.,.]]] => 11618 [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11666 [.,[[.,[[.,[.,.]],.]],[.,.]]] => 11682 [.,[[.,[[[.,.],.],.]],[.,.]]] => 11714 [.,[[[.,.],[.,[.,.]]],[.,.]]] => 11858 [.,[[[.,.],[[.,.],.]],[.,.]]] => 11874 [.,[[[.,[.,.]],[.,.]],[.,.]]] => 11922 [.,[[[[.,.],.],[.,.]],[.,.]]] => 12050 [.,[[[.,[.,[.,.]]],.],[.,.]]] => 11938 [.,[[[.,[[.,.],.]],.],[.,.]]] => 11970 [.,[[[[.,.],[.,.]],.],[.,.]]] => 12066 [.,[[[[.,[.,.]],.],.],[.,.]]] => 12098 [.,[[[[[.,.],.],.],.],[.,.]]] => 12162 [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 11604 [.,[[.,[.,[.,[[.,.],.]]]],.]] => 11608 [.,[[.,[.,[[.,.],[.,.]]]],.]] => 11620 [.,[[.,[.,[[.,[.,.]],.]]],.]] => 11624 [.,[[.,[.,[[[.,.],.],.]]],.]] => 11632 [.,[[.,[[.,.],[.,[.,.]]]],.]] => 11668 [.,[[.,[[.,.],[[.,.],.]]],.]] => 11672 [.,[[.,[[.,[.,.]],[.,.]]],.]] => 11684 [.,[[.,[[[.,.],.],[.,.]]],.]] => 11716 [.,[[.,[[.,[.,[.,.]]],.]],.]] => 11688 [.,[[.,[[.,[[.,.],.]],.]],.]] => 11696 [.,[[.,[[[.,.],[.,.]],.]],.]] => 11720 [.,[[.,[[[.,[.,.]],.],.]],.]] => 11728 [.,[[.,[[[[.,.],.],.],.]],.]] => 11744 [.,[[[.,.],[.,[.,[.,.]]]],.]] => 11860 [.,[[[.,.],[.,[[.,.],.]]],.]] => 11864 [.,[[[.,.],[[.,.],[.,.]]],.]] => 11876 [.,[[[.,.],[[.,[.,.]],.]],.]] => 11880 [.,[[[.,.],[[[.,.],.],.]],.]] => 11888 [.,[[[.,[.,.]],[.,[.,.]]],.]] => 11924 [.,[[[.,[.,.]],[[.,.],.]],.]] => 11928 [.,[[[[.,.],.],[.,[.,.]]],.]] => 12052 [.,[[[[.,.],.],[[.,.],.]],.]] => 12056 [.,[[[.,[.,[.,.]]],[.,.]],.]] => 11940 [.,[[[.,[[.,.],.]],[.,.]],.]] => 11972 [.,[[[[.,.],[.,.]],[.,.]],.]] => 12068 [.,[[[[.,[.,.]],.],[.,.]],.]] => 12100 [.,[[[[[.,.],.],.],[.,.]],.]] => 12164 [.,[[[.,[.,[.,[.,.]]]],.],.]] => 11944 [.,[[[.,[.,[[.,.],.]]],.],.]] => 11952 [.,[[[.,[[.,.],[.,.]]],.],.]] => 11976 [.,[[[.,[[.,[.,.]],.]],.],.]] => 11984 [.,[[[.,[[[.,.],.],.]],.],.]] => 12000 [.,[[[[.,.],[.,[.,.]]],.],.]] => 12072 [.,[[[[.,.],[[.,.],.]],.],.]] => 12080 [.,[[[[.,[.,.]],[.,.]],.],.]] => 12104 [.,[[[[[.,.],.],[.,.]],.],.]] => 12168 [.,[[[[.,[.,[.,.]]],.],.],.]] => 12112 [.,[[[[.,[[.,.],.]],.],.],.]] => 12128 [.,[[[[[.,.],[.,.]],.],.],.]] => 12176 [.,[[[[[.,[.,.]],.],.],.],.]] => 12192 [.,[[[[[[.,.],.],.],.],.],.]] => 12224 [[.,.],[.,[.,[.,[.,[.,.]]]]]] => 12970 [[.,.],[.,[.,[.,[[.,.],.]]]]] => 12972 [[.,.],[.,[.,[[.,.],[.,.]]]]] => 12978 [[.,.],[.,[.,[[.,[.,.]],.]]]] => 12980 [[.,.],[.,[.,[[[.,.],.],.]]]] => 12984 [[.,.],[.,[[.,.],[.,[.,.]]]]] => 13002 [[.,.],[.,[[.,.],[[.,.],.]]]] => 13004 [[.,.],[.,[[.,[.,.]],[.,.]]]] => 13010 [[.,.],[.,[[[.,.],.],[.,.]]]] => 13026 [[.,.],[.,[[.,[.,[.,.]]],.]]] => 13012 [[.,.],[.,[[.,[[.,.],.]],.]]] => 13016 [[.,.],[.,[[[.,.],[.,.]],.]]] => 13028 [[.,.],[.,[[[.,[.,.]],.],.]]] => 13032 [[.,.],[.,[[[[.,.],.],.],.]]] => 13040 [[.,.],[[.,.],[.,[.,[.,.]]]]] => 13098 [[.,.],[[.,.],[.,[[.,.],.]]]] => 13100 [[.,.],[[.,.],[[.,.],[.,.]]]] => 13106 [[.,.],[[.,.],[[.,[.,.]],.]]] => 13108 [[.,.],[[.,.],[[[.,.],.],.]]] => 13112 [[.,.],[[.,[.,.]],[.,[.,.]]]] => 13130 [[.,.],[[.,[.,.]],[[.,.],.]]] => 13132 [[.,.],[[[.,.],.],[.,[.,.]]]] => 13194 [[.,.],[[[.,.],.],[[.,.],.]]] => 13196 [[.,.],[[.,[.,[.,.]]],[.,.]]] => 13138 [[.,.],[[.,[[.,.],.]],[.,.]]] => 13154 [[.,.],[[[.,.],[.,.]],[.,.]]] => 13202 [[.,.],[[[.,[.,.]],.],[.,.]]] => 13218 [[.,.],[[[[.,.],.],.],[.,.]]] => 13250 [[.,.],[[.,[.,[.,[.,.]]]],.]] => 13140 [[.,.],[[.,[.,[[.,.],.]]],.]] => 13144 [[.,.],[[.,[[.,.],[.,.]]],.]] => 13156 [[.,.],[[.,[[.,[.,.]],.]],.]] => 13160 [[.,.],[[.,[[[.,.],.],.]],.]] => 13168 [[.,.],[[[.,.],[.,[.,.]]],.]] => 13204 [[.,.],[[[.,.],[[.,.],.]],.]] => 13208 [[.,.],[[[.,[.,.]],[.,.]],.]] => 13220 [[.,.],[[[[.,.],.],[.,.]],.]] => 13252 [[.,.],[[[.,[.,[.,.]]],.],.]] => 13224 [[.,.],[[[.,[[.,.],.]],.],.]] => 13232 [[.,.],[[[[.,.],[.,.]],.],.]] => 13256 [[.,.],[[[[.,[.,.]],.],.],.]] => 13264 [[.,.],[[[[[.,.],.],.],.],.]] => 13280 [[.,[.,.]],[.,[.,[.,[.,.]]]]] => 13482 [[.,[.,.]],[.,[.,[[.,.],.]]]] => 13484 [[.,[.,.]],[.,[[.,.],[.,.]]]] => 13490 [[.,[.,.]],[.,[[.,[.,.]],.]]] => 13492 [[.,[.,.]],[.,[[[.,.],.],.]]] => 13496 [[.,[.,.]],[[.,.],[.,[.,.]]]] => 13514 [[.,[.,.]],[[.,.],[[.,.],.]]] => 13516 [[.,[.,.]],[[.,[.,.]],[.,.]]] => 13522 [[.,[.,.]],[[[.,.],.],[.,.]]] => 13538 [[.,[.,.]],[[.,[.,[.,.]]],.]] => 13524 [[.,[.,.]],[[.,[[.,.],.]],.]] => 13528 [[.,[.,.]],[[[.,.],[.,.]],.]] => 13540 [[.,[.,.]],[[[.,[.,.]],.],.]] => 13544 [[.,[.,.]],[[[[.,.],.],.],.]] => 13552 [[[.,.],.],[.,[.,[.,[.,.]]]]] => 14506 [[[.,.],.],[.,[.,[[.,.],.]]]] => 14508 [[[.,.],.],[.,[[.,.],[.,.]]]] => 14514 [[[.,.],.],[.,[[.,[.,.]],.]]] => 14516 [[[.,.],.],[.,[[[.,.],.],.]]] => 14520 [[[.,.],.],[[.,.],[.,[.,.]]]] => 14538 [[[.,.],.],[[.,.],[[.,.],.]]] => 14540 [[[.,.],.],[[.,[.,.]],[.,.]]] => 14546 [[[.,.],.],[[[.,.],.],[.,.]]] => 14562 [[[.,.],.],[[.,[.,[.,.]]],.]] => 14548 [[[.,.],.],[[.,[[.,.],.]],.]] => 14552 [[[.,.],.],[[[.,.],[.,.]],.]] => 14564 [[[.,.],.],[[[.,[.,.]],.],.]] => 14568 [[[.,.],.],[[[[.,.],.],.],.]] => 14576 [[.,[.,[.,.]]],[.,[.,[.,.]]]] => 13610 [[.,[.,[.,.]]],[.,[[.,.],.]]] => 13612 [[.,[.,[.,.]]],[[.,.],[.,.]]] => 13618 [[.,[.,[.,.]]],[[.,[.,.]],.]] => 13620 [[.,[.,[.,.]]],[[[.,.],.],.]] => 13624 [[.,[[.,.],.]],[.,[.,[.,.]]]] => 13866 [[.,[[.,.],.]],[.,[[.,.],.]]] => 13868 [[.,[[.,.],.]],[[.,.],[.,.]]] => 13874 [[.,[[.,.],.]],[[.,[.,.]],.]] => 13876 [[.,[[.,.],.]],[[[.,.],.],.]] => 13880 [[[.,.],[.,.]],[.,[.,[.,.]]]] => 14634 [[[.,.],[.,.]],[.,[[.,.],.]]] => 14636 [[[.,.],[.,.]],[[.,.],[.,.]]] => 14642 [[[.,.],[.,.]],[[.,[.,.]],.]] => 14644 [[[.,.],[.,.]],[[[.,.],.],.]] => 14648 [[[.,[.,.]],.],[.,[.,[.,.]]]] => 14890 [[[.,[.,.]],.],[.,[[.,.],.]]] => 14892 [[[.,[.,.]],.],[[.,.],[.,.]]] => 14898 [[[.,[.,.]],.],[[.,[.,.]],.]] => 14900 [[[.,[.,.]],.],[[[.,.],.],.]] => 14904 [[[[.,.],.],.],[.,[.,[.,.]]]] => 15402 [[[[.,.],.],.],[.,[[.,.],.]]] => 15404 [[[[.,.],.],.],[[.,.],[.,.]]] => 15410 [[[[.,.],.],.],[[.,[.,.]],.]] => 15412 [[[[.,.],.],.],[[[.,.],.],.]] => 15416 [[.,[.,[.,[.,.]]]],[.,[.,.]]] => 13642 [[.,[.,[.,[.,.]]]],[[.,.],.]] => 13644 [[.,[.,[[.,.],.]]],[.,[.,.]]] => 13706 [[.,[.,[[.,.],.]]],[[.,.],.]] => 13708 [[.,[[.,.],[.,.]]],[.,[.,.]]] => 13898 [[.,[[.,.],[.,.]]],[[.,.],.]] => 13900 [[.,[[.,[.,.]],.]],[.,[.,.]]] => 13962 [[.,[[.,[.,.]],.]],[[.,.],.]] => 13964 [[.,[[[.,.],.],.]],[.,[.,.]]] => 14090 [[.,[[[.,.],.],.]],[[.,.],.]] => 14092 [[[.,.],[.,[.,.]]],[.,[.,.]]] => 14666 [[[.,.],[.,[.,.]]],[[.,.],.]] => 14668 [[[.,.],[[.,.],.]],[.,[.,.]]] => 14730 [[[.,.],[[.,.],.]],[[.,.],.]] => 14732 [[[.,[.,.]],[.,.]],[.,[.,.]]] => 14922 [[[.,[.,.]],[.,.]],[[.,.],.]] => 14924 [[[[.,.],.],[.,.]],[.,[.,.]]] => 15434 [[[[.,.],.],[.,.]],[[.,.],.]] => 15436 [[[.,[.,[.,.]]],.],[.,[.,.]]] => 14986 [[[.,[.,[.,.]]],.],[[.,.],.]] => 14988 [[[.,[[.,.],.]],.],[.,[.,.]]] => 15114 [[[.,[[.,.],.]],.],[[.,.],.]] => 15116 [[[[.,.],[.,.]],.],[.,[.,.]]] => 15498 [[[[.,.],[.,.]],.],[[.,.],.]] => 15500 [[[[.,[.,.]],.],.],[.,[.,.]]] => 15626 [[[[.,[.,.]],.],.],[[.,.],.]] => 15628 [[[[[.,.],.],.],.],[.,[.,.]]] => 15882 [[[[[.,.],.],.],.],[[.,.],.]] => 15884 [[.,[.,[.,[.,[.,.]]]]],[.,.]] => 13650 [[.,[.,[.,[[.,.],.]]]],[.,.]] => 13666 [[.,[.,[[.,.],[.,.]]]],[.,.]] => 13714 [[.,[.,[[.,[.,.]],.]]],[.,.]] => 13730 [[.,[.,[[[.,.],.],.]]],[.,.]] => 13762 [[.,[[.,.],[.,[.,.]]]],[.,.]] => 13906 [[.,[[.,.],[[.,.],.]]],[.,.]] => 13922 [[.,[[.,[.,.]],[.,.]]],[.,.]] => 13970 [[.,[[[.,.],.],[.,.]]],[.,.]] => 14098 [[.,[[.,[.,[.,.]]],.]],[.,.]] => 13986 [[.,[[.,[[.,.],.]],.]],[.,.]] => 14018 [[.,[[[.,.],[.,.]],.]],[.,.]] => 14114 [[.,[[[.,[.,.]],.],.]],[.,.]] => 14146 [[.,[[[[.,.],.],.],.]],[.,.]] => 14210 [[[.,.],[.,[.,[.,.]]]],[.,.]] => 14674 [[[.,.],[.,[[.,.],.]]],[.,.]] => 14690 [[[.,.],[[.,.],[.,.]]],[.,.]] => 14738 [[[.,.],[[.,[.,.]],.]],[.,.]] => 14754 [[[.,.],[[[.,.],.],.]],[.,.]] => 14786 [[[.,[.,.]],[.,[.,.]]],[.,.]] => 14930 [[[.,[.,.]],[[.,.],.]],[.,.]] => 14946 [[[[.,.],.],[.,[.,.]]],[.,.]] => 15442 [[[[.,.],.],[[.,.],.]],[.,.]] => 15458 [[[.,[.,[.,.]]],[.,.]],[.,.]] => 14994 [[[.,[[.,.],.]],[.,.]],[.,.]] => 15122 [[[[.,.],[.,.]],[.,.]],[.,.]] => 15506 [[[[.,[.,.]],.],[.,.]],[.,.]] => 15634 [[[[[.,.],.],.],[.,.]],[.,.]] => 15890 [[[.,[.,[.,[.,.]]]],.],[.,.]] => 15010 [[[.,[.,[[.,.],.]]],.],[.,.]] => 15042 [[[.,[[.,.],[.,.]]],.],[.,.]] => 15138 [[[.,[[.,[.,.]],.]],.],[.,.]] => 15170 [[[.,[[[.,.],.],.]],.],[.,.]] => 15234 [[[[.,.],[.,[.,.]]],.],[.,.]] => 15522 [[[[.,.],[[.,.],.]],.],[.,.]] => 15554 [[[[.,[.,.]],[.,.]],.],[.,.]] => 15650 [[[[[.,.],.],[.,.]],.],[.,.]] => 15906 [[[[.,[.,[.,.]]],.],.],[.,.]] => 15682 [[[[.,[[.,.],.]],.],.],[.,.]] => 15746 [[[[[.,.],[.,.]],.],.],[.,.]] => 15938 [[[[[.,[.,.]],.],.],.],[.,.]] => 16002 [[[[[[.,.],.],.],.],.],[.,.]] => 16130 [[.,[.,[.,[.,[.,[.,.]]]]]],.] => 13652 [[.,[.,[.,[.,[[.,.],.]]]]],.] => 13656 [[.,[.,[.,[[.,.],[.,.]]]]],.] => 13668 [[.,[.,[.,[[.,[.,.]],.]]]],.] => 13672 [[.,[.,[.,[[[.,.],.],.]]]],.] => 13680 [[.,[.,[[.,.],[.,[.,.]]]]],.] => 13716 [[.,[.,[[.,.],[[.,.],.]]]],.] => 13720 [[.,[.,[[.,[.,.]],[.,.]]]],.] => 13732 [[.,[.,[[[.,.],.],[.,.]]]],.] => 13764 [[.,[.,[[.,[.,[.,.]]],.]]],.] => 13736 [[.,[.,[[.,[[.,.],.]],.]]],.] => 13744 [[.,[.,[[[.,.],[.,.]],.]]],.] => 13768 [[.,[.,[[[.,[.,.]],.],.]]],.] => 13776 [[.,[.,[[[[.,.],.],.],.]]],.] => 13792 [[.,[[.,.],[.,[.,[.,.]]]]],.] => 13908 [[.,[[.,.],[.,[[.,.],.]]]],.] => 13912 [[.,[[.,.],[[.,.],[.,.]]]],.] => 13924 [[.,[[.,.],[[.,[.,.]],.]]],.] => 13928 [[.,[[.,.],[[[.,.],.],.]]],.] => 13936 [[.,[[.,[.,.]],[.,[.,.]]]],.] => 13972 [[.,[[.,[.,.]],[[.,.],.]]],.] => 13976 [[.,[[[.,.],.],[.,[.,.]]]],.] => 14100 [[.,[[[.,.],.],[[.,.],.]]],.] => 14104 [[.,[[.,[.,[.,.]]],[.,.]]],.] => 13988 [[.,[[.,[[.,.],.]],[.,.]]],.] => 14020 [[.,[[[.,.],[.,.]],[.,.]]],.] => 14116 [[.,[[[.,[.,.]],.],[.,.]]],.] => 14148 [[.,[[[[.,.],.],.],[.,.]]],.] => 14212 [[.,[[.,[.,[.,[.,.]]]],.]],.] => 13992 [[.,[[.,[.,[[.,.],.]]],.]],.] => 14000 [[.,[[.,[[.,.],[.,.]]],.]],.] => 14024 [[.,[[.,[[.,[.,.]],.]],.]],.] => 14032 [[.,[[.,[[[.,.],.],.]],.]],.] => 14048 [[.,[[[.,.],[.,[.,.]]],.]],.] => 14120 [[.,[[[.,.],[[.,.],.]],.]],.] => 14128 [[.,[[[.,[.,.]],[.,.]],.]],.] => 14152 [[.,[[[[.,.],.],[.,.]],.]],.] => 14216 [[.,[[[.,[.,[.,.]]],.],.]],.] => 14160 [[.,[[[.,[[.,.],.]],.],.]],.] => 14176 [[.,[[[[.,.],[.,.]],.],.]],.] => 14224 [[.,[[[[.,[.,.]],.],.],.]],.] => 14240 [[.,[[[[[.,.],.],.],.],.]],.] => 14272 [[[.,.],[.,[.,[.,[.,.]]]]],.] => 14676 [[[.,.],[.,[.,[[.,.],.]]]],.] => 14680 [[[.,.],[.,[[.,.],[.,.]]]],.] => 14692 [[[.,.],[.,[[.,[.,.]],.]]],.] => 14696 [[[.,.],[.,[[[.,.],.],.]]],.] => 14704 [[[.,.],[[.,.],[.,[.,.]]]],.] => 14740 [[[.,.],[[.,.],[[.,.],.]]],.] => 14744 [[[.,.],[[.,[.,.]],[.,.]]],.] => 14756 [[[.,.],[[[.,.],.],[.,.]]],.] => 14788 [[[.,.],[[.,[.,[.,.]]],.]],.] => 14760 [[[.,.],[[.,[[.,.],.]],.]],.] => 14768 [[[.,.],[[[.,.],[.,.]],.]],.] => 14792 [[[.,.],[[[.,[.,.]],.],.]],.] => 14800 [[[.,.],[[[[.,.],.],.],.]],.] => 14816 [[[.,[.,.]],[.,[.,[.,.]]]],.] => 14932 [[[.,[.,.]],[.,[[.,.],.]]],.] => 14936 [[[.,[.,.]],[[.,.],[.,.]]],.] => 14948 [[[.,[.,.]],[[.,[.,.]],.]],.] => 14952 [[[.,[.,.]],[[[.,.],.],.]],.] => 14960 [[[[.,.],.],[.,[.,[.,.]]]],.] => 15444 [[[[.,.],.],[.,[[.,.],.]]],.] => 15448 [[[[.,.],.],[[.,.],[.,.]]],.] => 15460 [[[[.,.],.],[[.,[.,.]],.]],.] => 15464 [[[[.,.],.],[[[.,.],.],.]],.] => 15472 [[[.,[.,[.,.]]],[.,[.,.]]],.] => 14996 [[[.,[.,[.,.]]],[[.,.],.]],.] => 15000 [[[.,[[.,.],.]],[.,[.,.]]],.] => 15124 [[[.,[[.,.],.]],[[.,.],.]],.] => 15128 [[[[.,.],[.,.]],[.,[.,.]]],.] => 15508 [[[[.,.],[.,.]],[[.,.],.]],.] => 15512 [[[[.,[.,.]],.],[.,[.,.]]],.] => 15636 [[[[.,[.,.]],.],[[.,.],.]],.] => 15640 [[[[[.,.],.],.],[.,[.,.]]],.] => 15892 [[[[[.,.],.],.],[[.,.],.]],.] => 15896 [[[.,[.,[.,[.,.]]]],[.,.]],.] => 15012 [[[.,[.,[[.,.],.]]],[.,.]],.] => 15044 [[[.,[[.,.],[.,.]]],[.,.]],.] => 15140 [[[.,[[.,[.,.]],.]],[.,.]],.] => 15172 [[[.,[[[.,.],.],.]],[.,.]],.] => 15236 [[[[.,.],[.,[.,.]]],[.,.]],.] => 15524 [[[[.,.],[[.,.],.]],[.,.]],.] => 15556 [[[[.,[.,.]],[.,.]],[.,.]],.] => 15652 [[[[[.,.],.],[.,.]],[.,.]],.] => 15908 [[[[.,[.,[.,.]]],.],[.,.]],.] => 15684 [[[[.,[[.,.],.]],.],[.,.]],.] => 15748 [[[[[.,.],[.,.]],.],[.,.]],.] => 15940 [[[[[.,[.,.]],.],.],[.,.]],.] => 16004 [[[[[[.,.],.],.],.],[.,.]],.] => 16132 [[[.,[.,[.,[.,[.,.]]]]],.],.] => 15016 [[[.,[.,[.,[[.,.],.]]]],.],.] => 15024 [[[.,[.,[[.,.],[.,.]]]],.],.] => 15048 [[[.,[.,[[.,[.,.]],.]]],.],.] => 15056 [[[.,[.,[[[.,.],.],.]]],.],.] => 15072 [[[.,[[.,.],[.,[.,.]]]],.],.] => 15144 [[[.,[[.,.],[[.,.],.]]],.],.] => 15152 [[[.,[[.,[.,.]],[.,.]]],.],.] => 15176 [[[.,[[[.,.],.],[.,.]]],.],.] => 15240 [[[.,[[.,[.,[.,.]]],.]],.],.] => 15184 [[[.,[[.,[[.,.],.]],.]],.],.] => 15200 [[[.,[[[.,.],[.,.]],.]],.],.] => 15248 [[[.,[[[.,[.,.]],.],.]],.],.] => 15264 [[[.,[[[[.,.],.],.],.]],.],.] => 15296 [[[[.,.],[.,[.,[.,.]]]],.],.] => 15528 [[[[.,.],[.,[[.,.],.]]],.],.] => 15536 [[[[.,.],[[.,.],[.,.]]],.],.] => 15560 [[[[.,.],[[.,[.,.]],.]],.],.] => 15568 [[[[.,.],[[[.,.],.],.]],.],.] => 15584 [[[[.,[.,.]],[.,[.,.]]],.],.] => 15656 [[[[.,[.,.]],[[.,.],.]],.],.] => 15664 [[[[[.,.],.],[.,[.,.]]],.],.] => 15912 [[[[[.,.],.],[[.,.],.]],.],.] => 15920 [[[[.,[.,[.,.]]],[.,.]],.],.] => 15688 [[[[.,[[.,.],.]],[.,.]],.],.] => 15752 [[[[[.,.],[.,.]],[.,.]],.],.] => 15944 [[[[[.,[.,.]],.],[.,.]],.],.] => 16008 [[[[[[.,.],.],.],[.,.]],.],.] => 16136 [[[[.,[.,[.,[.,.]]]],.],.],.] => 15696 [[[[.,[.,[[.,.],.]]],.],.],.] => 15712 [[[[.,[[.,.],[.,.]]],.],.],.] => 15760 [[[[.,[[.,[.,.]],.]],.],.],.] => 15776 [[[[.,[[[.,.],.],.]],.],.],.] => 15808 [[[[[.,.],[.,[.,.]]],.],.],.] => 15952 [[[[[.,.],[[.,.],.]],.],.],.] => 15968 [[[[[.,[.,.]],[.,.]],.],.],.] => 16016 [[[[[[.,.],.],[.,.]],.],.],.] => 16144 [[[[[.,[.,[.,.]]],.],.],.],.] => 16032 [[[[[.,[[.,.],.]],.],.],.],.] => 16064 [[[[[[.,.],[.,.]],.],.],.],.] => 16160 [[[[[[.,[.,.]],.],.],.],.],.] => 16192 [[[[[[[.,.],.],.],.],.],.],.] => 16256 ----------------------------------------------------------------------------- Created: May 16, 2014 at 02:50 by Kyle Ryan ----------------------------------------------------------------------------- Last Updated: Dec 30, 2016 at 10:59 by Christian Stump