A323950 - OEIS

%I #10 Feb 10 2019 12:40:24

%S 1,1,1,2,6,12,23,44,82,149,267,475,841,1484,2613,4595,8074,14180,

%T 24896,43702,76705,134622,236260,414623,727629,1276917,2240851,

%U 3932438,6900967,12110373,21252244,37295110,65448378,114853920,201554603,353703696,620706742

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-3,1).

%F 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

%e The a(1) = 1 through a(5) = 12 partitions:

%e   {{1}}  {{1}{2}}  {{123}}      {{1234}}        {{12345}}

%e                    {{1}{2}{3}}  {{1}{234}}      {{1}{2345}}

%e                                 {{123}{4}}      {{1234}{5}}

%e                                 {{124}{3}}      {{1235}{4}}

%e                                 {{134}{2}}      {{1245}{3}}

%e                                 {{1}{2}{3}{4}}  {{1345}{2}}

%e                                                 {{1}{2}{345}}

%e                                                 {{1}{234}{5}}

%e                                                 {{123}{4}{5}}

%e                                                 {{125}{3}{4}}

%e                                                 {{145}{2}{3}}

%e                                                 {{1}{2}{3}{4}{5}}

%t 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]}]];

%t spsu[_,{}]:={{}};spsu[foo_,set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,___}];

%t Table[Length[spsu[cyceds[n,2],Range[n]]],{n,15}]

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

%K nonn,easy

%O 0,4

%A _Gus Wiseman_, Feb 10 2019

%E More terms from _Alois P. Heinz_, Feb 10 2019