A149561 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, 0), (-1, 0, 1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 59, 197, 893, 3303, 15137, 59095, 273663, 1105191, 5159271, 21336649, 100195667, 421818947, 1989617133, 8493738751, 40199221659, 173546936539, 823571270199, 3588440362341, 17066016528211, 74935974222697, 357019784911547, 1577978975863395, 7529231227050559, 33466788898535849

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149558 A149559 A149560 * A149562 A149563 A149564

Adjacent sequences: A149558 A149559 A149560 * A149562 A149563 A149564

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved