A149464 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, 0, 1), (-1, 1, 1), (0, 1, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 4, 13, 52, 209, 898, 3898, 17383, 78335, 358867, 1654507, 7705474, 36071044, 170031345, 804606129, 3825822908, 18249491754, 87362378973, 419284812428, 2017756629055, 9730792790577, 47027997052118, 227679959115481, 1104183474096156, 5362865745453707, 26083735725385808, 127023206715913660

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A097169 A149463 A323791 * A307398 A129147 A151476

Adjacent sequences: A149461 A149462 A149463 * A149465 A149466 A149467

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved