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A337021
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The number of n-step self avoiding walks on a 3D cubic lattice confined inside a box of size 2x2x2 where the walk starts at the center of the box.
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4
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1, 6, 24, 72, 168, 456, 1032, 2712, 5784, 14640, 29760, 71136, 133344, 291696, 479232, 950880, 1343088, 2375808, 2774832, 4266240, 3909792, 5046672, 3230400, 3316704, 1122000, 808128, 0
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OFFSET
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0,2
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LINKS
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FORMULA
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For n>=27 all terms are 0 as the walk contains more steps than there are available lattice points in the 2x2x2 box.
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EXAMPLE
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a(1) = 6 as the walk is free to move one step in all six axial directions.
a(2) = 24 as after a step in one of the six axial directions the walk must turn along the face of the box; this eliminates the 2-step straight walk in all directions, so the total number of walks is 6*5-6 = 24.
a(26) = 0 as it is not possible to visit all 26 available lattice points when the walk starts from the middle of the box.
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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