A148552 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), (-1, 0, 1), (-1, 1, -1), (-1, 1, 1), (1, 0, 0)}.

1, 1, 3, 5, 21, 44, 194, 447, 2059, 5054, 23760, 60785, 290185, 765374, 3688939, 9954865, 48328461, 132793952, 648110850, 1806922951, 8854881499, 24984984772, 122828350857, 350072375310, 1725363761048, 4959679647599, 24494419473314, 70931380591142, 350897963505759, 1022670848686661, 5066201743368781

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A148549 A148550 A148551 * A148553 A239795 A261272

Adjacent sequences: A148549 A148550 A148551 * A148553 A148554 A148555

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved