A150233 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, 0, 1), (1, -1, 0), (1, 1, 0)}.

1, 2, 6, 22, 82, 325, 1333, 5544, 23623, 101702, 442102, 1943860, 8596023, 38264599, 171359276, 770542923, 3480459008, 15778420195, 71751938260, 327315216072, 1496927922396, 6862255642186, 31529789003704, 145147832272060, 669428572072825, 3092751498980032, 14310325845463212, 66312151553326834

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, 1 + j, k, -1 + n] + aux[i, 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: A191755 A150231 A150232 * A150234 A150235 A150236

Adjacent sequences: A150230 A150231 A150232 * A150234 A150235 A150236

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved