A150970 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), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 36, 157, 710, 3257, 15115, 71008, 336214, 1599507, 7650782, 36747858, 177037977, 855315890, 4142700612, 20105493813, 97750570368, 476036133721, 2321534199609, 11335833550603, 55415731236055, 271183822714642, 1328308300376693, 6511887399486650, 31949044841913435, 156863573594043375

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[i, -1 + 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: A150968 A073156 A150969 * A150971 A150972 A150973

Adjacent sequences: A150967 A150968 A150969 * A150971 A150972 A150973

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved