A151214 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, -1), (1, 0, 1), (1, 1, 0), (1, 1, 1)}

1, 3, 13, 55, 257, 1173, 5641, 26589, 129649, 621779, 3055365, 14808965, 73117707, 356884157, 1767623943, 8670146633, 43036138213, 211849042763, 1053200775857, 5198497137737, 25873982027773, 127978528457705, 637530951171095, 3158574078412183, 15745161220951335, 78110901810505983

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A151212 A151213 A102287 * A151215 A151216 A151217

Adjacent sequences: A151211 A151212 A151213 * A151215 A151216 A151217

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved