A150334 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, 0, 0), (0, -1, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 23, 84, 320, 1246, 5066, 20658, 86447, 363905, 1551717, 6680516, 28928013, 126428930, 554487973, 2448780826, 10853451220, 48323714099, 215999075802, 968342883670, 4357205440631, 19650838467499, 88894872008197, 403000279608600, 1831245639619344, 8338814533961132, 38040367001178855

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A047002 A127497 A151291 * A150335 A150336 A173519

Adjacent sequences: A150331 A150332 A150333 * A150335 A150336 A150337

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved