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%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
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