A148936 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, 0), (0, 1, -1), (1, -1, 1), (1, 0, 1)}.

1, 1, 3, 9, 28, 102, 372, 1392, 5490, 21848, 88322, 364457, 1519209, 6394726, 27196992, 116596476, 503240096, 2185814374, 9549807525, 41930059192, 184918480762, 819029864816, 3641316550806, 16243317238849, 72693657655711, 326286683303623, 1468439616798464, 6625361546600399, 29962992825549341

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A148933 A148934 A148935 * A121656 A148937 A047137

Adjacent sequences: A148933 A148934 A148935 * A148937 A148938 A148939

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved