A151012 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, 0, 1), (0, -1, 1), (1, 1, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 39, 181, 864, 4167, 20276, 99611, 490674, 2425351, 12026527, 59713601, 296903002, 1478237657, 7364664103, 36715516955, 183156337486, 913991473905, 4562565733245, 22783244464539, 113789919999702, 568422308878305, 2839964161136580, 14190620411994443, 70914372566446584, 354412071129304385

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A151009 A151010 A151011 * A151013 A151014 A151015

Adjacent sequences: A151009 A151010 A151011 * A151013 A151014 A151015

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved