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A148424 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, -1), (-1, 1, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)} 0
1, 1, 2, 5, 18, 59, 235, 893, 3810, 15513, 68355, 291633, 1316392, 5780793, 26499220, 118934221, 551889602, 2515299167, 11775715141, 54333877955, 256237560742, 1193389613255, 5660224648326, 26567605325073, 126621506371332, 598025706185715, 2861510181706267, 13586615488837211, 65234679563225012 (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[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A148421 A148422 A148423 * A148425 A286317 A303174

Adjacent sequences:  A148421 A148422 A148423 * A148425 A148426 A148427

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 9 18:55 EDT 2022. Contains 356026 sequences. (Running on oeis4.)