A148660 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, 0), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}

1, 1, 3, 6, 25, 66, 277, 817, 3651, 11758, 52874, 178648, 823085, 2903549, 13436779, 48720169, 228260341, 849198384, 3991541312, 15120095518, 71589010237, 275869985842, 1309412900349, 5111198336392, 24375181571827, 96323446028493, 460270198243344, 1836571496934897, 8804730973938187

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148657 A148658 A148659 * A148661 A148662 A148663

Adjacent sequences: A148657 A148658 A148659 * A148661 A148662 A148663

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved