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Search: id:A151390
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| A151390 |
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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, 1), (0, 1), (1, -1)} |
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+0
1
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| 1, 1, 1, 2, 6, 13, 33, 88, 256, 706, 2150, 6274, 19646, 59393, 190957, 592500, 1940660, 6150996, 20448656, 65920110, 221846298, 725218554, 2465440766, 8154637122, 27960144414, 93407091930, 322618540398, 1087075564126, 3778473023706, 12827256622881, 44832392213325, 153201067563940, 538068545212932
(list; graph; listen)
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OFFSET
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0,4
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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[1 + i, -1 + 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: A003039 A109385 A098407 this_sequence A116426 A162057 A026550
Adjacent sequences: A151387 A151388 A151389 this_sequence A151391 A151392 A151393
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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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