A323950 Number of ways to split an n-cycle into connected subgraphs, none having exactly two vertices.

1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705, 134622, 236260, 414623, 727629, 1276917, 2240851, 3932438, 6900967, 12110373, 21252244, 37295110, 65448378, 114853920, 201554603, 353703696, 620706742

Offset

0,4

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-3,1).

Formula

G.f.: (x^7-3*x^6+3*x^5-2*x^4+x^3-3*x^2+3*x-1)/((x^3-x^2+2*x-1)*(x-1)^2). - Alois P. Heinz, Feb 10 2019

Example

The a(1) = 1 through a(5) = 12 partitions:
  {{1}}  {{1}{2}}  {{123}}      {{1234}}        {{12345}}
                   {{1}{2}{3}}  {{1}{234}}      {{1}{2345}}
                                {{123}{4}}      {{1234}{5}}
                                {{124}{3}}      {{1235}{4}}
                                {{134}{2}}      {{1245}{3}}
                                {{1}{2}{3}{4}}  {{1345}{2}}
                                                {{1}{2}{345}}
                                                {{1}{234}{5}}
                                                {{123}{4}{5}}
                                                {{125}{3}{4}}
                                                {{145}{2}{3}}
                                                {{1}{2}{3}{4}{5}}

Mathematica

cyceds[n_, k_]:=Union[Sort/@Join@@Table[1+Mod[Range[i, j]-1, n], {i, n}, {j, Prepend[Range[i+k, n+i-1], i]}]];
spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];
Table[Length[spsu[cyceds[n, 2], Range[n]]], {n, 15}]

Crossrefs

Cf. A000325, A001610, A001680, A005251, A066982, A306351, A323950, A323951, A323952, A323954.

Sequence in context: A192703 A192969 A294532 * A291014 A257479 A307740

Adjacent sequences: A323947 A323948 A323949 * A323951 A323952 A323953

Keyword

nonn,easy

Author

Gus Wiseman, Feb 10 2019

Extensions

More terms from Alois P. Heinz, Feb 10 2019

Status

approved