login
A279791
Number of twice-partitions of type (Q,R,Q) and weight n.
13
1, 1, 2, 2, 3, 6, 5, 8, 8, 16, 12, 23, 18, 36, 33, 50, 38, 84, 54, 106, 100, 155, 104, 244, 142, 301, 270, 436, 256, 684, 340, 788, 670, 1044, 585, 1868, 760, 1878, 1600, 2647
OFFSET
1,3
EXAMPLE
The a(8)=8 twice-partitions of type (Q,R,Q) are:
((8)), ((71)), ((62)), ((53)),
((521)), ((4)(31)), ((31)(4)), ((431)).
MATHEMATICA
nn=20;
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Total[Total[Factorial/@Length/@Select[sps[Sort[#]], SameQ@@Total/@#&]]&/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, nn}]
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Dec 18 2016
STATUS
approved