A150275 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, 0), (-1, 0, 0), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 23, 87, 344, 1430, 6006, 25638, 111108, 485979, 2144374, 9526239, 42581108, 191357708, 863551551, 3912874126, 17792811362, 81149740528, 371155976937, 1701830597050, 7820751344589, 36014935517232, 166162951039617, 767957329992987, 3554955243640582, 16480495255912614, 76507069324161891

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A217200 A110068 A247211 * A335537 A150276 A189043

Adjacent sequences: A150272 A150273 A150274 * A150276 A150277 A150278

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved