A150142 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, 0, 0), (0, 0, 1), (1, -1, 0), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 73, 282, 1131, 4672, 19724, 84752, 369429, 1629435, 7259192, 32615418, 147619128, 672411537, 3080081649, 14179056899, 65562383998, 304359944046, 1418000511407, 6627902117686, 31071410377680, 146056590528879, 688272817354702, 3250831753441245, 15386777437834858, 72971502660653682

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A104632 A194956 A150141 * A150143 A150144 A243255

Adjacent sequences: A150139 A150140 A150141 * A150143 A150144 A150145

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved