A150932 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), (0, 0, 1), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 2, 9, 33, 153, 644, 3079, 13796, 66951, 309900, 1516751, 7163139, 35252495, 168702164, 833311863, 4024832013, 19933067217, 96923446796, 480935723503, 2350317848041, 11679152784131, 57296876389616, 285034184537707, 1402601392007074, 6983561015163199, 34448127705013148, 171635610631292203

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150929 A150930 A150931 * A150933 A150934 A150935

Adjacent sequences: A150929 A150930 A150931 * A150933 A150934 A150935

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved