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A150675 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, 0), (-1, 0, -1), (1, 0, 1), (1, 1, 1)} 0
1, 2, 8, 26, 112, 414, 1842, 7242, 32804, 133800, 613052, 2562776, 11836532, 50365642, 234002666, 1009167634, 4710183476, 20528989512, 96167408220, 422736061420, 1986214533136, 8793033897180, 41416814340404, 184449324491236, 870624943393208, 3897129584472968, 18428316118385328, 82854571612170996 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A295934 A187151 A150674 * A150676 A150677 A150678

Adjacent sequences: A150672 A150673 A150674 * A150676 A150677 A150678

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 2 19:34 EST 2023. Contains 360024 sequences. (Running on oeis4.)