A148677 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, 1), (0, -1, 1), (1, 1, 0)}.

1, 1, 3, 7, 21, 67, 195, 653, 2099, 6933, 23423, 78535, 271285, 925973, 3206663, 11185071, 38983433, 137051515, 482479299, 1708206559, 6052735529, 21521991943, 76778794491, 274300787629, 982476049335, 3525512594021, 12682333972857, 45657403910329, 164716081204213, 595171088189807, 2153100164896935

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A105864 A130380 A097147 * A240506 A037127 A105795

Adjacent sequences: A148674 A148675 A148676 * A148678 A148679 A148680

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved