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A149614 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, 0, 0), (1, -1, 0), (1, 1, -1), (1, 1, 1)} 0
1, 1, 5, 15, 63, 241, 1029, 4235, 18455, 78715, 348351, 1519343, 6802653, 30136875, 136132599, 610143777, 2774845257, 12547858643, 57373751109, 261245486761, 1199829541531, 5493494482443, 25325015850429, 116475926371087, 538686575714645, 2486914898525215, 11533775470631997, 53418442775940213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[1 + i, j, 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: A149611 A149612 A149613 * A149615 A149616 A189945

Adjacent sequences:  A149611 A149612 A149613 * A149615 A149616 A149617

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 19 17:54 EDT 2021. Contains 348091 sequences. (Running on oeis4.)