A150853 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, 1, -1), (0, 1, 1), (1, -1, 0), (1, 0, 1)}.

1, 2, 8, 32, 140, 628, 2896, 13567, 64365, 308151, 1485833, 7204422, 35088850, 171518779, 840911474, 4132992702, 20355478219, 100429656440, 496242132791, 2455183619347, 12160650553525, 60290452100646, 299161592857493, 1485537573155445, 7381483420114541, 36698905370451628, 182550859120066383

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A179469 A150851 A150852 * A150854 A150855 A150856

Adjacent sequences: A150850 A150851 A150852 * A150854 A150855 A150856

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved