A150141 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, 1, -1), (0, 0, 1), (1, -1, 0), (1, 1, 0)}.

1, 2, 6, 20, 73, 281, 1132, 4668, 19721, 84781, 368971, 1627669, 7241241, 32500219, 146956243, 668357723, 3058153676, 14058081823, 64914531045, 300967681710, 1400214412893, 6536451108935, 30602252860171, 143666262628831, 676176061560358, 3189725718512715, 15079740230940998, 71431939122794444

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, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A192497 A104632 A194956 * A150142 A150143 A150144

Adjacent sequences: A150138 A150139 A150140 * A150142 A150143 A150144

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved