A149735 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, 0), (0, 1, -1), (1, -1, 1), (1, 1, 1)}

1, 1, 5, 17, 75, 309, 1425, 6201, 29221, 132289, 629579, 2912059, 13988935, 65633287, 317029795, 1503382545, 7293409299, 34848431283, 169636664131, 815377820679, 3979513299379, 19217458483101, 93997752125995, 455631560068157, 2232619470595959, 10855680648153653, 53274469970301121, 259704454769699575

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, -1 + 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, 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: A149732 A149733 A149734 * A149736 A145959 A126956

Adjacent sequences: A149732 A149733 A149734 * A149736 A149737 A149738

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved