A150011 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, 1), (-1, 0, 1), (0, 1, 0), (1, -1, -1), (1, 0, 1)}.

1, 2, 5, 17, 60, 226, 894, 3596, 14733, 61458, 259481, 1106753, 4764856, 20677287, 90314950, 396783369, 1752566181, 7776050081, 34641886875, 154916582579, 695094294939, 3128227114848, 14118442677861, 63883713196776, 289742429602369, 1317022255376015, 5998719802774542, 27374214721917542

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, -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: A150008 A150009 A150010 * A360211 A112832 A148415

Adjacent sequences: A150008 A150009 A150010 * A150012 A150013 A150014

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved