A149468 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, 1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 13, 54, 212, 916, 3984, 17758, 80159, 367710, 1700619, 7930388, 37241889, 175959334, 835236876, 3981398689, 19051204957, 91454768190, 440232013360, 2124509433674, 10275936003671, 49800985817062, 241783261316646, 1175778895993067, 5726143038966814, 27923583090576487, 136335309089326590

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, -1 + 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: A082570 A145208 A149467 * A149469 A229182 A149470

Adjacent sequences: A149465 A149466 A149467 * A149469 A149470 A149471

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved