A150777 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), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 30, 130, 564, 2557, 11683, 54346, 254545, 1203147, 5716624, 27310772, 130979508, 630438224, 3043186518, 14727732882, 71430873409, 347119061240, 1689676501553, 8237284859214, 40211183449288, 196532448155539, 961599134863745, 4709587019390239, 23086704003927488, 113265637193121309

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, k, -1 + n] + aux[-1 + i, 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: A150774 A150775 A150776 * A150778 A150779 A150780

Adjacent sequences: A150774 A150775 A150776 * A150778 A150779 A150780

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved