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A151504
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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), (-1, 1), (0, -1), (1, 0)}
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0
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1, 0, 2, 1, 10, 12, 70, 139, 607, 1602, 6152, 18933, 69198, 231382, 835638, 2924153, 10602298, 38116310, 139479988, 510483372, 1887183843, 6997718116, 26119506819, 97854304825, 368400345109, 1391981776521, 5280261360181, 20096390417468, 76739852267440, 293910546549621, 1128904523397628, 4347615932984721
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MATHEMATICA
| 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[1 + 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
| Sequence in context: A138098 A163914 A167883 * A151507 A151363 A196130
Adjacent sequences: A151501 A151502 A151503 * A151505 A151506 A151507
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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