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A151503
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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), (1, -1), (1, 0)}
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0
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1, 0, 1, 1, 3, 6, 17, 40, 117, 314, 912, 2667, 7916, 23963, 73586, 227611, 715444, 2262450, 7223397, 23261164, 75343490, 245847919, 806839587, 2661738663, 8829581024, 29418789715, 98457806482, 330890849398, 1116135299721, 3778754481148, 12835824454442, 43738283921029, 149490351563243, 512353843888497
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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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[-1 + 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
| Sequence in context: A024315 A049943 A027415 * A007718 A089264 A121399
Adjacent sequences: A151500 A151501 A151502 * A151504 A151505 A151506
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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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