A148638 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, 1, -1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 6, 22, 61, 233, 733, 2947, 10104, 41604, 150819, 634383, 2395210, 10223510, 39801121, 171943819, 685615395, 2990420051, 12155736895, 53444047859, 220699421489, 976862543867, 4087516321436, 18196407921064, 76994974494165, 344467263811475, 1471591422477907, 6612456796697229

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A148635 A148636 A148637 * A148639 A148640 A148641

Adjacent sequences: A148635 A148636 A148637 * A148639 A148640 A148641

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved