A150982 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, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 36, 175, 778, 3845, 17905, 89001, 424172, 2113948, 10209253, 50948157, 248113556, 1239102385, 6068403739, 30319281508, 149081622109, 745044873005, 3674283188050, 18365478315123, 90776305283804, 453782651352721, 2246903663540931, 11232846424037632, 55697767257067913, 278460200211505251

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, 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: A150980 A137955 A150981 * A003161 A305206 A101610

Adjacent sequences: A150979 A150980 A150981 * A150983 A150984 A150985

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved