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A149502 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (-1, 1, -1), (1, -1, -1), (1, 1, 1)} 0
1, 1, 5, 9, 45, 121, 581, 1817, 8797, 29313, 142301, 503977, 2453477, 8974977, 43860725, 165014649, 808021149, 3105881545, 15244653845, 59564679569, 292834353069, 1161030410585, 5716228788437, 22923441010793, 113003432141573, 457852354530881, 2259301849434869, 9233277980486313, 45605218569509805 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A100305 A149500 A149501 * A219701 A088974 A105182

Adjacent sequences:  A149499 A149500 A149501 * A149503 A149504 A149505

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 18 23:44 EDT 2021. Contains 348071 sequences. (Running on oeis4.)