A149423 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, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 56, 211, 1025, 4307, 21204, 94266, 467078, 2145817, 10669555, 50053958, 249384307, 1186640955, 5919439517, 28450917045, 142033418623, 687720200014, 3434955791348, 16724912981263, 83563256781361, 408630153079305, 2042102527291284, 10020026867440662, 50081965879762276, 246408793434070306

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[-1 + 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: A051195 A179607 A149422 * A295496 A164575 A124004

Adjacent sequences: A149420 A149421 A149422 * A149424 A149425 A149426

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved