A151015 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, 0), (0, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 39, 183, 868, 4197, 20444, 100317, 494358, 2444531, 12116607, 60169249, 299205662, 1489478285, 7421004919, 36998103731, 184554402390, 920984156829, 4597556967587, 22957329604823, 114660204573360, 572774287555053, 2861670392922102, 14299128414676793, 71456889590284654, 357121243412106029

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A151012 A151013 A151014 * A151016 A151017 A151018

Adjacent sequences: A151012 A151013 A151014 * A151016 A151017 A151018

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved