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 A337367 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The corresponding number of n-step walks is given in A173380. REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes the sequence A173380). LINKS Table of n, a(n) for n=0..28. Sequence Fans Mailing list, discussion of the sequence A173380, November 2010. EXAMPLE The allowed 4-step walks with their associated end-to-end square distances are: . + 10 4 | 8 8 8 16 +--+ + +--+ + + X--+---+---+---+ | | | 10 | | + + + +--+--+ +--+ + +--+ 10 + 10 | | | | | | | | X--+ X--+ X--+ X--+ X--+ X--+--+ X--+--+ X--+--+--+ . 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. CROSSREFS Cf. A173380, A001411. Sequence in context: A302267 A113154 A302966 * A334323 A270161 A270977 Adjacent sequences: A337364 A337365 A337366 * A337368 A337369 A337370 KEYWORD nonn,walk AUTHOR Scott R. Shannon, Aug 25 2020 STATUS approved

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Last modified August 10 15:26 EDT 2024. Contains 375056 sequences. (Running on oeis4.)