A150511 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, 1), (0, 0, 1), (0, 1, -1), (1, -1, 1), (1, 0, 1)}.

1, 2, 7, 25, 102, 421, 1835, 8068, 36463, 165906, 766789, 3562740, 16714944, 78749841, 373407046, 1776555853, 8490305807, 40686783270, 195617231802, 942606575327, 4553378965810, 22036254471516, 106852979603759, 518923028545648, 2524046047179717, 12292867020315560, 59946635460333394, 292653126601321637

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150508 A150509 A150510 * A036784 A221456 A221457

Adjacent sequences: A150508 A150509 A150510 * A150512 A150513 A150514

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved