A151050 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), (0, 0, 1), (1, 0, 0), (1, 0, 1)}.

1, 3, 10, 37, 143, 585, 2465, 10616, 46464, 206309, 927790, 4212640, 19276458, 88787800, 411449663, 1916848749, 8970470541, 42143168591, 198683134963, 939706509220, 4457357557544, 21197120026557, 101037186925055, 482627967442833, 2309934392488989, 11075673413214807, 53193324686695579

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + 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: A211975 A357399 A219260 * A151051 A164044 A119244

Adjacent sequences: A151047 A151048 A151049 * A151051 A151052 A151053

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved