A151076 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, 1, -1), (0, 1, 0), (1, 0, 0), (1, 0, 1)}.

1, 3, 10, 40, 172, 752, 3417, 15861, 74103, 351352, 1681640, 8076015, 39063800, 189889216, 924922052, 4523125805, 22183456842, 108940260148, 536282913395, 2644780657087, 13054897004324, 64540176018987, 319455186011981, 1582213202208502, 7844634619098689, 38926073651463768, 193245536619581965

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A088300 A151074 A151075 * A151077 A300043 A258973

Adjacent sequences: A151073 A151074 A151075 * A151077 A151078 A151079

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved