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Search: id:A151425
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| A151425 |
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (0, 1), (1, -1)} |
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+0
1
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| 1, 1, 2, 4, 11, 28, 82, 242, 752, 2379, 7750, 25692, 86635, 296558, 1027851, 3603503, 12758718, 45585878, 164181411, 595669369, 2175535954, 7994009929, 29537993178, 109704376600, 409377743815, 1534371295481, 5774424726514, 21814125817926, 82700717070725, 314575421938613, 1200315307181211, 4593459795047725
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OFFSET
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0,3
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LINKS
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M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MATHEMATICA
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aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A005200 A148133 A148134 this_sequence A148135 A034768 A148136
Adjacent sequences: A151422 A151423 A151424 this_sequence A151426 A151427 A151428
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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