A150553 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, 1), (-1, 1, 1), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 26, 105, 443, 1931, 8619, 39138, 180100, 837279, 3924640, 18519066, 87870877, 418876055, 2004669434, 9626561780, 46363330956, 223866924604, 1083384848069, 5253395542429, 25519189279554, 124160104067499, 604945683243907, 2951277482140430, 14414887009758621, 70481444130319621

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A150550 A150551 A150552 * A150554 A150555 A151297

Adjacent sequences: A150550 A150551 A150552 * A150554 A150555 A150556

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved