A149085 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, -1, 1), (-1, 0, 0), (1, -1, -1), (1, 1, 0)}.

1, 1, 4, 7, 30, 69, 293, 809, 3382, 10439, 43701, 143573, 607068, 2074221, 8852116, 31177563, 133899322, 483528703, 2086264777, 7687404457, 33298955306, 124729199423, 542093742204, 2058678763143, 8972283179552, 34477413838191, 150612967540901, 584671713820833, 2559233654640368

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A149082 A149083 A149084 * A149086 A149087 A149088

Adjacent sequences: A149082 A149083 A149084 * A149086 A149087 A149088

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved