A148119 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, 0, 0), (-1, 1, -1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 11, 26, 70, 205, 606, 1772, 5659, 18055, 57650, 190806, 643903, 2158908, 7409215, 25810603, 89837412, 316495463, 1130343744, 4037596315, 14539324740, 52909811198, 192837217446, 706592984332, 2611271049921, 9668148544321, 35939545700694, 134514159833921, 504483895185584, 1897880107311959

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A151257 A148117 A148118 * A148120 A148121 A148122

Adjacent sequences: A148116 A148117 A148118 * A148120 A148121 A148122

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved