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

1,3

Links

Table of n, a(n) for n=1..40.

Gus Wiseman, Sequences enumerating triangles of integer partitions

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

Cf. A063834, A275972, A279790.

Sequence in context: A116447 A137757 A210751 * A328744 A345706 A132886

Adjacent sequences: A279788 A279789 A279790 * A279792 A279793 A279794

Keyword

nonn,look

Author

Gus Wiseman, Dec 18 2016

Status

approved