A151075 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), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 3, 10, 40, 169, 729, 3249, 14717, 67436, 312803, 1461936, 6878212, 32557918, 154799224, 739043897, 3540956927, 17015609718, 81988739469, 395987808269, 1916493786483, 9292986559674, 45136611500778, 219563958375717, 1069533315247073, 5216387240816365, 25470886932498859, 124501742320960825

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A287887 A088300 A151074 * A151076 A151077 A300043

Adjacent sequences: A151072 A151073 A151074 * A151076 A151077 A151078

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved