A150273 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, -1, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 22, 92, 364, 1598, 6824, 30404, 136764, 617446, 2831276, 13031622, 60346428, 281845432, 1316928654, 6197429960, 29231903134, 138286736940, 656927696126, 3123870663170, 14906011474554, 71252038551888, 341159241443052, 1637518071666842, 7866975262786576, 37870754508194960, 182537355530341254

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A107591 A279569 A155866 * A342292 A303923 A264868

Adjacent sequences: A150270 A150271 A150272 * A150274 A150275 A150276

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved