A150393 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, 1), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 24, 90, 361, 1467, 6228, 26685, 116295, 515285, 2297850, 10381454, 47140567, 215572145, 992487194, 4586657093, 21320447629, 99417329814, 465335801616, 2185945802704, 10293561464046, 48628823142478, 230216553972385, 1092420725825020, 5195384613357609, 24749785914532161, 118143629535180508

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A150391 A378585 A150392 * A150394 A151294 A196470

Adjacent sequences: A150390 A150391 A150392 * A150394 A150395 A150396

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved