A151044 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), (0, 1, 1), (1, 0, 0)}.

1, 3, 9, 33, 129, 516, 2150, 9129, 39208, 170844, 751739, 3329775, 14854617, 66658383, 300429493, 1359788478, 6178043489, 28156202058, 128688253311, 589725931525, 2708660600493, 12467109806982, 57493840683072, 265605179665083, 1228989585714965, 5695220219094839, 26428445184643521, 122796644702539179

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, k, -1 + n] + aux[i, -1 + 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: A087289 A084508 A151043 * A247195 A236408 A217617

Adjacent sequences: A151041 A151042 A151043 * A151045 A151046 A151047

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved