A149289 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), (0, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 11, 44, 168, 684, 2917, 12434, 54952, 244134, 1100482, 5016090, 23007212, 106468234, 495348425, 2317147904, 10893890888, 51410034690, 243569360712, 1157680823330, 5518485716846, 26378212854558, 126380662190358, 606859223002138, 2919830896866662, 14073944474518660, 67953617541129074

Offset

0,3

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, 1 + k, -1 + n] + aux[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: A149286 A149287 A149288 * A149290 A074410 A359707

Adjacent sequences: A149286 A149287 A149288 * A149290 A149291 A149292

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved