A150292 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), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 23, 93, 397, 1743, 7835, 35746, 165186, 770599, 3622718, 17138997, 81505690, 389304925, 1866373874, 8976096969, 43288108887, 209262664063, 1013747551292, 4920151811424, 23919322278143, 116457079657159, 567760445594646, 2771349016260029, 13542414273198623, 66242681480812979

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, -1 + 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: A012866 A150290 A150291 * A191721 A150293 A370285

Adjacent sequences: A150289 A150290 A150291 * A150293 A150294 A150295

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved