A150272 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, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 6, 22, 91, 388, 1703, 7660, 34923, 160928, 749625, 3520625, 16630720, 78987346, 376981894, 1805927651, 8678665702, 41831396697, 202142233159, 978882886268, 4749539961933, 23085904421970, 112385181441367, 547858441522134, 2674144171401459, 13067816933126466, 63924801052463888, 313005077923122789

Offset

0,2

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A226435 A292318 A150271 * A342289 A124293 A341382

Adjacent sequences: A150269 A150270 A150271 * A150273 A150274 A150275

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved