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Search: id:A151404
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| A151404 |
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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, 0), (0, -1), (0, 1), (1, -1)} |
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+0
1
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| 1, 1, 2, 4, 9, 23, 58, 160, 447, 1280, 3799, 11329, 34648, 107194, 335052, 1062809, 3392928, 10944072, 35576811, 116369798, 383517144, 1270497711, 4232708951, 14174190320, 47670133454, 161055621043, 546226400383, 1859448826545, 6352403850949, 21770237036258, 74841611960045, 258025290079584, 891972398224757
(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[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, 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: A159330 A159331 A135346 this_sequence A027071 A027133 A032010
Adjacent sequences: A151401 A151402 A151403 this_sequence A151405 A151406 A151407
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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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