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A151493
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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, -1), (1, 0), (1, 1)}
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0
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1, 1, 6, 20, 114, 529, 3050, 16333, 96291, 554489, 3343913, 20074658, 123474818, 761154695, 4758617798, 29876386844, 189275072084, 1204491672779, 7713591678563, 49602001416920, 320478996972260, 2078111745252647, 13525786891484513, 88309928176783985, 578342399955533489, 3797738127548969927
(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, -1 + j, -1 + 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] + 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: A151485 A191424 A200538 * A036755 A045470 A117998
Adjacent sequences: A151490 A151491 A151492 * A151494 A151495 A151496
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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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