A149128 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, -1, 1), (-1, 0, 1), (0, 0, -1), (1, 1, 0)}.

1, 1, 4, 9, 34, 104, 382, 1339, 4988, 18544, 70850, 271890, 1060528, 4161164, 16487268, 65749179, 263892516, 1065095388, 4320942050, 17607151198, 72053673624, 295956572780, 1219869663596, 5044142750342, 20918319018672, 86986781478112, 362640691240052, 1515363972162724, 6346212269965344

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149126 A149127 A163069 * A149129 A149130 A149131

Adjacent sequences: A149125 A149126 A149127 * A149129 A149130 A149131

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved