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A292884 Number of ways to shuffle together a multiset of compositions to form a composition of n. 0
1, 3, 8, 25, 76, 248, 806, 2714, 9205, 31846, 111185, 393224 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 23:02 EDT 2018. Contains 316431 sequences. (Running on oeis4.)