A292884 Number of ways to shuffle together a multiset of compositions to form a composition of n.

1, 3, 8, 25, 76, 248, 806, 2714, 9205, 31846, 111185, 393224

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Example

The a(3)=8 shuffles are:
(111)<=((111)), (111)<=((1)(11)), (111)<=((1)(1)(1)),
(12)<=((12)), (12)<=((1)(2)),
(21)<=((21)), (21)<=((1)(2)),
(3)<=((3)).

Mathematica

nn=10;
comps[0]:={{}}; comps[n_]:=Join@@Table[Prepend[#, i]&/@comps[n-i], {i, n}];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
dealings[q_]:=Union[Function[ptn, Sort[q[[#]]&/@ptn]]/@sps[Range[Length[q]]]];
Table[Total[Length/@dealings/@comps[n]], {n, nn}]

Crossrefs

Cf. A034691, A059966, A060223, A269134.

Sequence in context: A148788 A292778 A022553 * A148789 A088327 A148790

Adjacent sequences: A292881 A292882 A292883 * A292885 A292886 A292887

Keyword

nonn,more

Author

Gus Wiseman, Sep 26 2017

Extensions

a(12) from Robert Price, Sep 16 2018

Status

approved