A279791 Number of twice-partitions of type (Q,R,Q) and weight n.

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

Author

Gus Wiseman, Dec 18 2016

Keywords

• nonn
• look

Examples

			The a(8)=8 twice-partitions of type (Q,R,Q) are:
((8)), ((71)), ((62)), ((53)),
((521)), ((4)(31)), ((31)(4)), ((431)).
		

Links

• Gus Wiseman, Sequences enumerating triangles of integer partitions

Crossrefs

Cf. A063834, A275972, A279790.

Programs

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}]