A150222 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), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 21, 84, 341, 1417, 6096, 26748, 119130, 536341, 2438024, 11173211, 51593216, 239712120, 1119135769, 5247643747, 24707480877, 116758305908, 553480178855, 2630922475987, 12537514482770, 59887238868738, 286669943190835, 1374858224677984, 6605224484874324, 31784815003296123, 153181681050731848

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[i, -1 + j, 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: A178325 A087649 A328435 * A150223 A150224 A150225

Adjacent sequences: A150219 A150220 A150221 * A150223 A150224 A150225

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved