A149422 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, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 56, 208, 996, 4078, 19847, 86165, 422862, 1903766, 9391229, 43308943, 214368865, 1005327565, 4987734204, 23678524804, 117672616437, 563791036407, 2805257695526, 13536119727544, 67414254046586, 327111783619820, 1630286325643540, 7945974905609362, 39623933066496998, 193826942329261434

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, -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: A149421 A051195 A179607 * A149423 A295496 A164575

Adjacent sequences: A149419 A149420 A149421 * A149423 A149424 A149425

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved