A151202 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, 0, -1), (0, 1, 0), (1, 0, 1), (1, 1, 1)}

1, 3, 12, 53, 244, 1142, 5435, 26144, 126718, 617570, 3022461, 14841629, 73073082, 360547644, 1782074892, 8821006283, 43715724013, 216871664197, 1076829646939, 5350766870064, 26605134973704, 132360505109957, 658815651617991, 3280618909581023, 16342250157966834, 81435392340178751

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A151199 A151200 A151201 * A151203 A262442 A026781

Adjacent sequences: A151199 A151200 A151201 * A151203 A151204 A151205

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved