A150434 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, 0), (-1, 0, 1), (1, -1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 24, 99, 383, 1662, 6887, 30424, 131019, 586670, 2581368, 11680736, 52145590, 237672626, 1072548623, 4915035993, 22359367481, 102919456563, 471087278575, 2176372641684, 10010910854388, 46390466191967, 214249259241312, 995409647245975, 4612586140509972, 21478598420867456, 99809819411171975

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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A197554 A325581 A162044 * A150435 A150436 A197553

Adjacent sequences: A150431 A150432 A150433 * A150435 A150436 A150437

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved