A148611 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, 0, 1), (-1, 1, -1), (1, -1, 0), (1, 0, 1)}.

1, 1, 3, 6, 21, 53, 202, 573, 2294, 7006, 28850, 92846, 390092, 1303794, 5562947, 19142342, 82613977, 291006973, 1267423687, 4549911567, 19966824583, 72818698095, 321535722525, 1188494266831, 5275334545623, 19724654497789, 87947837063125, 332138900116759, 1486679487455533, 5664070305670293

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148608 A148609 A148610 * A148612 A098511 A354734

Adjacent sequences: A148608 A148609 A148610 * A148612 A148613 A148614

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved