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A151472
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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), (0, -1), (0, 1), (1, -1), (1, 0)}
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0
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1, 1, 3, 9, 30, 110, 423, 1687, 6984, 29574, 128074, 564652, 2527292, 11463972, 52602015, 243824807, 1140448152, 5377337150, 25539196048, 122093592944, 587170555168, 2839207157456, 13797304069674, 67357039620092, 330225541717108, 1625329978935340, 8028874036140468, 39796190100237612
(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, 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: A032125 A091699 A129167 * A107379 A117428 A134168
Adjacent sequences: A151469 A151470 A151471 * A151473 A151474 A151475
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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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