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A336862
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Table read by antidiagonals: T(h,n) is the number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2h X 2h X 2h where the walk starts at the middle of the box's edge.
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4
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4, 12, 4, 40, 14, 4, 118, 54, 14, 4, 358, 208, 56, 14, 4, 936, 826, 224, 56, 14, 4, 2600, 3232, 936, 226, 56, 14, 4, 6212, 12688, 3862, 956, 226, 56, 14, 4, 16068, 48924, 16196, 4026, 958, 226, 56, 14, 4, 34936, 187276, 67346, 17246, 4050, 958, 226, 56, 14, 4
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OFFSET
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1,1
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LINKS
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FORMULA
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For n >= (2h+1)^3, T(h,n) = 0 as the walk contains more steps than there are available lattice points in the 2h X 2h X 2h box.
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EXAMPLE
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T(1,2) = 12. A first step along either edge leading to the corner leaves two possible second steps. A first step to the center of either face can be followed by a second step to three edges or to the center of the box, four steps in all. Thus the total number of 2-step walks is 2*2+2*4 = 12.
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The table begins:
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4 12 40 118 358 936 2600 6212 16068 34936 83708 163452 357056...
4 14 54 208 826 3232 12688 48924 187276 705196 2627950 9670620 35231628...
4 14 56 224 936 3862 16196 67346 282676 1180326 4950936 20646098 86165926...
4 14 56 226 956 4026 17246 73588 316456 1358518 5860464 25266192 109288486...
4 14 56 226 958 4050 17478 75288 327778 1425340 6236152 27260378 119641050...
4 14 56 226 958 4052 17506 75600 330362 1444544 6360718 28020896 123963354...
4 14 56 226 958 4052 17508 75632 330766 1448280 6391426 28238732 125405300...
4 14 56 226 958 4052 17508 75634 330802 1448788 6396618 28285548 125766436...
4 14 56 226 958 4052 17508 75634 330804 1448828 6397242 28292536 125835068...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397286 28293288 125844228...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293336 125845120...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293338 125845172...
4 14 56 226 958 4052 17508 75634 330804 1448830 6397288 28293338 125845174...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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