A151061 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, 1, 0), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 3, 10, 38, 152, 639, 2771, 12281, 55420, 253364, 1171092, 5460007, 25639273, 121123086, 575076889, 2742195363, 13124176867, 63014222585, 303403995443, 1464445137864, 7083898807342, 34333188959553, 166690360145487, 810559968736787, 3947049979314502, 19244917231144970, 93943277175860158

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 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: A308124 A151059 A151060 * A109085 A259690 A001002

Adjacent sequences: A151058 A151059 A151060 * A151062 A151063 A151064

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved