A150901 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), (0, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 34, 160, 754, 3666, 17828, 87802, 432614, 2144172, 10631688, 52874430, 263050196, 1310789336, 6533453750, 32594854752, 162645656080, 812023451302, 4054706349966, 20253091836044, 101174456223766, 505520044421592, 2526042977404856, 12624066188909514, 63093298395691332, 315357996330544112

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

Crossrefs

Sequence in context: A150900 A084207 A151305 * A046649 A174808 A109972

Adjacent sequences: A150898 A150899 A150900 * A150902 A150903 A150904

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved