A150778 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, 0), (0, 1, -1), (1, 0, 0), (1, 1, 1)}

1, 2, 8, 30, 130, 568, 2569, 11745, 54532, 255124, 1203652, 5710145, 27228958, 130366881, 626386210, 3018558459, 14584522337, 70625103916, 342682597315, 1665668968272, 8109013544995, 39532920013144, 192975385335712, 943071629690735, 4613628029421766, 22592076543219255, 110726347729418356

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150775 A150776 A150777 * A150779 A150780 A150781

Adjacent sequences: A150775 A150776 A150777 * A150779 A150780 A150781

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved