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Search: id:A151370
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| A151370 |
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Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 1)} |
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+0
1
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| 1, 0, 2, 3, 20, 60, 345, 1400, 7770, 36876, 204876, 1062600, 5984352, 32772168, 187727826, 1065491427, 6206538910, 36123454224, 213645926208, 1266954939822, 7593846587496, 45694598654640, 277066122022872, 1686973019649060, 10331412410444280, 63524084460496480, 392411097399517800
(list; graph; listen)
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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, 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[aux[0, 0, n], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A136886 A072472 A055814 this_sequence A041567 A087301 A007113
Adjacent sequences: A151367 A151368 A151369 this_sequence A151371 A151372 A151373
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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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