A149515 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), (0, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 49, 157, 629, 2319, 9165, 35923, 144111, 579277, 2349989, 9611139, 39510403, 163374651, 677811085, 2823210939, 11813207247, 49554650923, 208578981839, 879510914225, 3719688553993, 15765286759389, 66957773740445, 284868978268515, 1213922356670815, 5182375308499355

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[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, 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: A142238 A370769 A149514 * A149516 A149517 A149518

Adjacent sequences: A149512 A149513 A149514 * A149516 A149517 A149518

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved