A149294 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, 0), (-1, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 46, 149, 659, 2359, 10786, 40881, 190323, 748193, 3527018, 14249557, 67783120, 279469503, 1338252962, 5605159863, 26979650007, 114453030191, 553174729286, 2371327312233, 11499306561012, 49727063025279, 241807843147514, 1053464596134725, 5134560174599273, 22512757056138723

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, 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, j, 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: A149291 A149292 A149293 * A149295 A149296 A149297

Adjacent sequences: A149291 A149292 A149293 * A149295 A149296 A149297

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved