A149671 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, 1), (0, 0, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 17, 63, 259, 1067, 4457, 19191, 82841, 362233, 1598323, 7088617, 31667685, 142110015, 640483695, 2899395681, 13163953953, 59965256157, 273940539817, 1254326068887, 5757231255235, 26479800661155, 122016618174329, 563255251234927, 2604287666051211, 12059299339779457, 55919399667456419

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, j, 1 + k, -1 + n] + aux[1 + i, 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: A149668 A149669 A149670 * A366978 A275220 A062229

Adjacent sequences: A149668 A149669 A149670 * A149672 A149673 A149674

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved