A148528 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, 0), (-1, -1, 1), (-1, 1, -1), (1, -1, -1), (1, 1, 0)}.

1, 1, 3, 5, 19, 39, 155, 369, 1511, 3999, 16699, 47411, 201035, 598115, 2566823, 7913909, 34278307, 108842863, 474944507, 1544928203, 6783383171, 22505843739, 99339846735, 335133673283, 1485928136875, 5085855937575, 22637540649467, 78461484523687, 350429147683243, 1228025277796767, 5501219119637891

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A148525 A148526 A148527 * A148529 A148530 A148531

Adjacent sequences: A148525 A148526 A148527 * A148529 A148530 A148531

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved