A151212 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), (0, 0, -1), (0, 0, 1), (0, 1, 1), (1, 1, 1)}.

1, 3, 13, 55, 249, 1135, 5275, 24727, 116855, 555601, 2654321, 12732069, 61274953, 295727069, 1430727417, 6936363189, 33690805225, 163906989103, 798574185487, 3895818006991, 19027958776871, 93035484993511, 455330249621399, 2230438627640211, 10934740863086635, 53648006249077831, 263391103222289955

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 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: A117376 A264037 A151318 * A151213 A102287 A151214

Adjacent sequences: A151209 A151210 A151211 * A151213 A151214 A151215

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved