A148496 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, 1), (-1, 1, 1), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 6, 22, 77, 297, 1158, 4760, 19615, 83170, 354235, 1537155, 6694459, 29509806, 130528377, 582259997, 2605232262, 11727542598, 52934218258, 240011811917, 1090827330717, 4974968161528, 22736645871636, 104197523836178, 478387995974963, 2201255167550108, 10145122325618120, 46842914075663584

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A014334 A107239 A262068 * A217528 A181367 A106434

Adjacent sequences: A148493 A148494 A148495 * A148497 A148498 A148499

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved