A149726 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, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 289, 1313, 5581, 25945, 114835, 540599, 2453645, 11667077, 53909213, 258252995, 1208508337, 5821455827, 27500611031, 133046370535, 633165453019, 3073897588439, 14714918458313, 71641305195307, 344591510346845, 1681643831688457, 8120575130056213, 39708177224041729, 192383235475270681

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 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: A149723 A149724 A149725 * A149727 A149728 A149729

Adjacent sequences: A149723 A149724 A149725 * A149727 A149728 A149729

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved