A148784 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), (0, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 8, 24, 79, 261, 886, 3129, 11101, 39877, 146007, 536573, 1986096, 7430086, 27875577, 105068168, 398612268, 1515643014, 5781406946, 22147965265, 84995804118, 326938348756, 1261326963966, 4873034768699, 18859268767095, 73145144603108, 284014204228567, 1104273212508320, 4300431280470938

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + 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: A118099 A066350 A375086 * A148785 A148786 A215576

Adjacent sequences: A148781 A148782 A148783 * A148785 A148786 A148787

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved