A149465 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, 0, 1), (0, 0, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 13, 53, 201, 840, 3574, 15657, 68851, 307490, 1388692, 6344965, 29161051, 134782622, 626411797, 2927546988, 13742107029, 64735935244, 305917618200, 1450175440663, 6894191053917, 32856878608281, 156932879198304, 751070728564779, 3601468236987239, 17299977132250675, 83234577482537502

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[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A129147 A151476 A140454 * A149466 A369226 A006604

Adjacent sequences: A149462 A149463 A149464 * A149466 A149467 A149468

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved