A151211 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), (-1, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 1)}

1, 3, 13, 53, 251, 1123, 5443, 25319, 124085, 589525, 2907101, 13992377, 69260281, 336246069, 1668515057, 8149453349, 40508704195, 198730129755, 989055732315, 4868337933007, 24251331823247, 119677240767379, 596579249085239, 2950013134883235, 14713426845193475, 72874410714058567, 363620465475437771

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + 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: A052990 A151209 A151210 * A367755 A121240 A065839

Adjacent sequences: A151208 A151209 A151210 * A151212 A151213 A151214

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved