A150010 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, 1), (0, 1, 0), (1, -1, -1), (1, 0, 1)}.

1, 2, 5, 17, 60, 226, 894, 3568, 14593, 60774, 255405, 1088287, 4680842, 20270594, 88477666, 388406999, 1713712621, 7599271318, 33835186549, 151220870639, 678235333756, 3051277234793, 13766822178955, 62276897969003, 282398247564030, 1283429063755581, 5844908741209452, 26669699058543416

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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150007 A150008 A150009 * A150011 A360211 A112832

Adjacent sequences: A150007 A150008 A150009 * A150011 A150012 A150013

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved