A149225 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, 0), (1, -1, 1), (1, 1, -1), (1, 1, 0)}

1, 1, 4, 10, 44, 150, 683, 2629, 12205, 50241, 236366, 1015593, 4822869, 21335021, 102023865, 460878520, 2215801954, 10167652064, 49093076267, 228011894094, 1104751698373, 5180228863652, 25171214811317, 118941071795246, 579343805179914, 2754893742189018, 13446312307968009, 64276239562116266

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A264571 A149223 A149224 * A122648 A058819 A052394

Adjacent sequences: A149222 A149223 A149224 * A149226 A149227 A149228

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved