A149441 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, 0, 0), (-1, 1, 1), (0, -1, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 13, 47, 179, 723, 2955, 12326, 52379, 225379, 979595, 4293370, 18968055, 84312906, 376849710, 1692411474, 7633371175, 34557396610, 156972861920, 715191169953, 3267419728346, 14964429086384, 68690122349498, 315956770424266, 1456075080616578, 6722003654277533, 31082482470824247

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A055451 A163862 A149440 * A149442 A078468 A354339

Adjacent sequences: A149438 A149439 A149440 * A149442 A149443 A149444

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved