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A151483
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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), (0, 1), (1, -1), (1, 0)}
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0
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1, 1, 4, 12, 48, 192, 832, 3712, 17152, 81152, 392192, 1928192, 9621504, 48623616, 248463360, 1282031616, 6672285696, 34993274880, 184793432064, 981947645952, 5247335399424, 28185150357504, 152104870084608, 824404913160192, 4486067252101120, 24501262150008832, 134274187559698432, 738200201575006208
(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[-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] + 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: A149385 A092898 A110594 * A192622 A111930 A197867
Adjacent sequences: A151480 A151481 A151482 * A151484 A151485 A151486
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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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