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A306351 Number of ways to split an n-cycle into connected subgraphs all having at least 4 vertices.

%I A306351 #11 Feb 10 2019 19:36:27
%S A306351 1,0,0,0,1,1,1,1,5,10,16,23,35,53,78,111,157,222,313,438,610,848,1178,
%T A306351 1634,2263,3131,4330,5986,8272,11427,15782,21794,30093,41548,57359,
%U A306351 79183,109307,150887,208279,287496,396838,547761,756077,1043611,1440488,1988289
%N A306351 Number of ways to split an n-cycle into connected subgraphs all having at least 4 vertices.
%H A306351 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-2,1).
%F A306351 G.f.: (2*x^9-3*x^8+x^3-3*x^2+3*x-1)/((x^4+x-1)*(x-1)^2). - _Alois P. Heinz_, Feb 10 2019
%e A306351 The a(7) = 1 through a(9) = 10 partitions:
%e A306351   {{1234567}}  {{12345678}}    {{123456789}}
%e A306351                {{1234}{5678}}  {{1234}{56789}}
%e A306351                {{1238}{4567}}  {{12345}{6789}}
%e A306351                {{1278}{3456}}  {{12349}{5678}}
%e A306351                {{1678}{2345}}  {{12389}{4567}}
%e A306351                                {{1239}{45678}}
%e A306351                                {{12789}{3456}}
%e A306351                                {{1289}{34567}}
%e A306351                                {{16789}{2345}}
%e A306351                                {{1789}{23456}}
%t A306351 cycedsprop[n_,k_]:=Union[Sort/@Join@@Table[1+Mod[Range[i,j]-1,n],{i,n},{j,i+k,n+i-1}]];
%t A306351 spsu[_,{}]:={{}};spsu[foo_,set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,___}];
%t A306351 Table[Length[spsu[cycedsprop[n,3],Range[n]]],{n,15}]
%Y A306351 Column k = 3 of A323954.
%Y A306351 Cf. A000325, A005251, A066982, A078012, A323950, A323951, A323953.
%K A306351 nonn,easy
%O A306351 0,9
%A A306351 _Gus Wiseman_, Feb 10 2019
%E A306351 More terms from _Alois P. Heinz_, Feb 10 2019