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A151501
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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), (-1, 1), (0, -1), (1, 0)}
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0
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1, 0, 2, 1, 8, 12, 45, 113, 341, 1018, 3095, 9555, 30324, 95537, 309763, 1002577, 3285362, 10859463, 36025440, 120586518, 405317722, 1369340161, 4651457133, 15854097472, 54284662488, 186521139750, 642995941300, 2224213237576, 7715127092600, 26838793844166, 93608792582527, 327272805790058, 1146930142662274
(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]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
| Sequence in context: A118708 A055134 A137370 * A102735 A088960 A121360
Adjacent sequences: A151498 A151499 A151500 * A151502 A151503 A151504
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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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