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Search: id:A151496
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| A151496 |
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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), (0, 1), (1, -1), (1, 0), (1, 1)} |
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+0
1
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| 1, 1, 7, 27, 160, 870, 5345, 32865, 211512, 1380372, 9214548, 62327958, 427516056, 2963478804, 20745401391, 146427786219, 1041261685464, 7453015732448, 53661092431232, 388397497629284, 2824677704718896, 20632192727484936, 151301370605585252, 1113568687159297278, 8223216946375477960
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OFFSET
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0,3
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LINKS
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M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MATHEMATICA
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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[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
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Sequence in context: A118101 A147996 A034536 this_sequence A035081 A003148 A033910
Adjacent sequences: A151493 A151494 A151495 this_sequence A151497 A151498 A151499
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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