A150486 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, 2, 7, 25, 100, 412, 1760, 7682, 34121, 153694, 699674, 3214634, 14878044, 69300335, 324524864, 1526826465, 7212569244, 34193106665, 162613538217, 775521788639, 3707866519259, 17767965677543, 85318197648386, 410444681087519, 1977907519106388, 9546268236852395, 46140569622347460, 223308638978809198

Offset

0,2

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: A150483 A150484 A150485 * A150487 A150488 A150489

Adjacent sequences: A150483 A150484 A150485 * A150487 A150488 A150489

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved