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A151046 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), (0, 0, 1), (0, 1, 0), (1, 0, 0)} 0
1, 3, 10, 35, 132, 516, 2086, 8585, 36040, 153062, 658558, 2856372, 12502898, 55051180, 244048234, 1086807005, 4865282682, 21858557906, 98615835998, 446208697638, 2025834611380, 9219765801128, 42078391465174, 192434838953262, 882143776302436, 4050904714495496, 18639979286877834 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A149037 A228769 A296164 * A221130 A084781 A151047

Adjacent sequences:  A151043 A151044 A151045 * A151047 A151048 A151049

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 13 17:54 EDT 2020. Contains 335689 sequences. (Running on oeis4.)