A150451 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, 0), (1, 1, 0)}.

1, 2, 7, 24, 104, 418, 1926, 8362, 39639, 179449, 864607, 4017001, 19549917, 92409184, 452737250, 2165952708, 10660736477, 51450505184, 254081698922, 1234291362727, 6110444134488, 29832800411044, 147965866991147, 725242808016821, 3602291161240133, 17711335237534464, 88072367031402318

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, 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: A256492 A150449 A150450 * A150452 A330254 A375129

Adjacent sequences: A150448 A150449 A150450 * A150452 A150453 A150454

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved