A148616 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, 0, 0), (-1, 0, 1), (0, -1, 0), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 6, 21, 58, 214, 710, 2688, 9935, 38635, 151986, 608873, 2484076, 10237368, 42773905, 180478226, 768102528, 3300273601, 14267425390, 62167686036, 272375280535, 1200459543480, 5318560273764, 23671746317505, 105850549499759, 475168208076953, 2141450914325080, 9684922332757176

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A148613 A148614 A148615 * A148617 A148618 A148619

Adjacent sequences: A148613 A148614 A148615 * A148617 A148618 A148619

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved