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A148543 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), (-1, 1, -1), (1, -1, 0), (1, 1, 0)} 0
1, 1, 3, 5, 19, 45, 173, 449, 1855, 5419, 22327, 67507, 289295, 931453, 3969825, 12998177, 56872875, 193906079, 843340791, 2901823841, 12869556293, 45583222801, 200960786165, 715524927773, 3203762549077, 11662542878931, 51920684241331, 189565536433271, 854843879121203, 3176982730594645 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[-1 + i, 1 + j, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A148540 A148541 A148542 * A148544 A148545 A065964

Adjacent sequences:  A148540 A148541 A148542 * A148544 A148545 A148546

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)