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A323951 Number of ways to split an n-cycle into connected subgraphs, all having at least three vertices.

%I A323951 #9 Feb 10 2019 12:40:55
%S A323951 1,0,0,1,1,1,4,8,13,22,36,56,86,131,197,294,437,647,955,1407,2070,
%T A323951 3042,4467,6556,9618,14106,20684,30325,44455,65164,95515,139997,
%U A323951 205189,300733,440760,645980,946745,1387538,2033552,2980332,4367906,6401495,9381865,13749810
%N A323951 Number of ways to split an n-cycle into connected subgraphs, all having at least three vertices.
%H A323951 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-2,1).
%F A323951 G.f.: (x^7-2*x^6+x^3-3*x^2+3*x-1)/((x^3+x-1)*(x-1)^2). - _Alois P. Heinz_, Feb 10 2019
%e A323951 The a(3) = 1 through a(7) = 8 partitions:
%e A323951   {{123}}  {{1234}}  {{12345}}  {{123456}}    {{1234567}}
%e A323951                                 {{123}{456}}  {{123}{4567}}
%e A323951                                 {{126}{345}}  {{1234}{567}}
%e A323951                                 {{156}{234}}  {{1237}{456}}
%e A323951                                               {{1267}{345}}
%e A323951                                               {{127}{3456}}
%e A323951                                               {{1567}{234}}
%e A323951                                               {{167}{2345}}
%t A323951 cycedsprop[n_,k_]:=Union[Sort/@Join@@Table[1+Mod[Range[i,j]-1,n],{i,n},{j,i+k,n+i-1}]];
%t A323951 spsu[_,{}]:={{}};spsu[foo_,set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,___}];
%t A323951 Table[Length[spsu[cycedsprop[n,2],Range[n]]],{n,15}]
%Y A323951 Cf. A000325, A001610, A001680, A005251, A066982, A306351, A323950, A323952, A323954.
%K A323951 nonn,easy
%O A323951 0,7
%A A323951 _Gus Wiseman_, Feb 10 2019
%E A323951 More terms from _Alois P. Heinz_, Feb 10 2019