A149771 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, 0), (1, 1, 1)}.

1, 1, 5, 19, 77, 317, 1361, 6025, 27163, 122675, 559209, 2573479, 11947959, 55780987, 261418223, 1229568863, 5807019993, 27526376675, 130867422041, 623691585535, 2979036324403, 14259880993181, 68396092991087, 328645441292561, 1581696320168591, 7623580934949633, 36795101748555815, 177818427231306201

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, 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: A268815 A108981 A228678 * A149772 A370194 A149773

Adjacent sequences: A149768 A149769 A149770 * A149772 A149773 A149774

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved