A149602 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, -1), (0, 1, -1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 15, 61, 221, 967, 3881, 16899, 70221, 315047, 1354407, 6082311, 26520757, 120929241, 536544351, 2448727261, 10949317877, 50429415865, 227885979067, 1050361492137, 4769636868583, 22118009769063, 101146482471553, 469341868210259, 2153448614138777, 10035909521465269, 46278020575454063

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A369555 A207969 A149601 * A149603 A149604 A149605

Adjacent sequences: A149599 A149600 A149601 * A149603 A149604 A149605

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved