A150699 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, 0), (-1, 0, 1), (-1, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 26, 120, 445, 2129, 8395, 40865, 167087, 820858, 3437518, 16979808, 72329288, 358522822, 1546934617, 7685725419, 33496603906, 166690839148, 732392833745, 3648822613213, 16139479515758, 80474841728532, 357966273352554, 1785996689525898, 7982779328398710, 39846874192191992, 178846571568017737

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A150696 A150697 A150698 * A150700 A150701 A150702

Adjacent sequences: A150696 A150697 A150698 * A150700 A150701 A150702

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved