A150566 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, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 107, 455, 2012, 9074, 41594, 192924, 903470, 4262270, 20231693, 96516302, 462374120, 2222933809, 10719593222, 51828194331, 251155772898, 1219515591916, 5931946148833, 28899291120181, 140988919633962, 688697812814343, 3367946840981885, 16487263285545995, 80786492334172444

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, 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: A150563 A150564 A150565 * A150567 A000151 A150568

Adjacent sequences: A150563 A150564 A150565 * A150567 A150568 A150569

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved