A148138 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), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 28, 90, 268, 915, 2932, 10533, 35993, 133691, 474722, 1807930, 6638026, 25794275, 97001870, 382848116, 1469545267, 5877102305, 22926929344, 92687064938, 366654371191, 1496182410466, 5987580859882, 24628481175790, 99564544617860, 412404734561672, 1681734278449444, 7008640582381384

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, 1 + k, -1 + n] + aux[-1 + i, j, 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: A034768 A148136 A148137 * A005503 A148139 A336871

Adjacent sequences: A148135 A148136 A148137 * A148139 A148140 A148141

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved