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Search: id:A151443
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| A151443 |
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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, -1), (1, 1)} |
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+0
1
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| 1, 1, 3, 6, 23, 57, 241, 667, 2966, 8784, 40295, 124964, 585435, 1877481, 8929621, 29378968, 141326855, 474458386, 2302594186, 7857845926, 38404279674, 132849003739, 653019772711, 2284925239463, 11285159305890, 39875000613009, 197732358849821, 704607036495398, 3505978390793893
(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, -1 + j, -1 + n] + aux[-1 + i, 1 + 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: A049415 A029848 A090910 this_sequence A148643 A148644 A148645
Adjacent sequences: A151440 A151441 A151442 this_sequence A151444 A151445 A151446
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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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