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A337367
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Sum of square end-to-end distance over all self-avoiding n-step walks on a square lattice where no adjacent points are allowed, except those for consecutive steps.
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0
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0, 4, 32, 156, 608, 2116, 6816, 20844, 61376, 175628, 491248, 1349172, 3650144, 9751532, 25774672, 67501556, 175375136, 452454276, 1160098576, 2958123556, 7505767840, 18959922796, 47701159264, 119570463980, 298719578688, 743984084700, 1847709517360, 4576818079076, 11309417827072
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OFFSET
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0,2
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COMMENTS
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The corresponding number of n-step walks is given in A173380.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes the sequence A173380).
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LINKS
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EXAMPLE
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The allowed 4-step walks with their associated end-to-end square distances are:
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+ 10
4 | 8 8 8 16
+--+ + +--+ + + X--+---+---+---+
| | | 10 | |
+ + + +--+--+ +--+ + +--+ 10 + 10
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X--+ X--+ X--+ X--+ X--+ X--+--+ X--+--+ X--+--+--+
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The eight non-straight walks sum to 68, and these can be walked in eight ways on the square lattice. The remaining straight walk can be walking in four ways. Thus a(4) = 68 * 8 + 16 * 4 = 608.
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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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