A148592 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), (-1, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 6, 20, 57, 191, 647, 2204, 7992, 28194, 104874, 384720, 1449306, 5483215, 20898490, 80658514, 311364894, 1216690972, 4756274956, 18748495518, 74099975703, 294247939801, 1173264704275, 4690663672229, 18833731765177, 75769138632263, 305949783943704, 1237810577381054, 5022401265853285

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + k, -1 + n] + aux[1 + 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: A148590 A363592 A148591 * A148593 A148594 A148595

Adjacent sequences: A148589 A148590 A148591 * A148593 A148594 A148595

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved