A150391 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, 0), (0, 1, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 24, 89, 355, 1419, 5945, 25173, 108323, 474325, 2089856, 9325373, 41890594, 189466107, 862964951, 3948140988, 18162054954, 83889968239, 388973082359, 1810306902559, 8450619905407, 39569513960496, 185773212627528, 874328973636940, 4124633701976350, 19498320345967292, 92359428407806574

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A150390 A383573 A052705 * A378585 A150392 A150393

Adjacent sequences: A150388 A150389 A150390 * A150392 A150393 A150394

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved