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Search: id:A151412
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| A151412 |
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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), (0, -1), (0, 1), (1, 0)} |
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+0
1
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| 1, 1, 3, 7, 21, 63, 198, 648, 2148, 7303, 25159, 87771, 309885, 1103217, 3961285, 14322270, 52098790, 190586734, 700547511, 2586505466, 9587737311, 35667671240, 133128177959, 498385063314, 1870940572326, 7041423384111, 26563151794983, 100425970551436, 380444157541490, 1443958508666422
(list; graph; listen)
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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, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[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: A148672 A148673 A141495 this_sequence A121797 A109361 A052805
Adjacent sequences: A151409 A151410 A151411 this_sequence A151413 A151414 A151415
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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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