A148427 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, 0, 0), (0, 1, 0), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 18, 62, 238, 916, 3706, 15243, 64409, 276189, 1203838, 5305479, 23641944, 106267870, 481560161, 2197119864, 10086780977, 46558844757, 215964339529, 1006146037229, 4706126682598, 22091433526799, 104041065742422, 491452327197918, 2327802367903136, 11053557370505303, 52609476576750227

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148426 A321099 A241894 * A068000 A148428 A266833

Adjacent sequences: A148424 A148425 A148426 * A148428 A148429 A148430

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved