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%I #9 Sep 18 2019 21:33:37
%S 1,1,1,2,6,21,7,10,10,15,15,21,21,28,28,36,36,45,45,55,55,66,66,78,78,
%T 91,91,105,105,120,120,136,136,153,153,171,171,190,190,210,210,231,
%U 231,253,253,276,276,300,300,325,325,351,351,378,378,406,406,435,435,465,465,496
%N Number of 3-indecomposable (connected) graphs on n nodes.
%C See A124593 for definition.
%H Colin Barker, <a href="/A126099/b126099.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F G.f.: x/((1-x)*(1-x^2)^2) + 1 - x^3 + 3*x^4 + 15*x^5 + x^6.
%F From _Colin Barker_, May 27 2016: (Start)
%F a(n) = (-1+(-1)^n+2*(1+(-1)^n)*n+2*n^2)/16 for n>7.
%F a(n) = (n^2+2*n)/8 for n>7 and even.
%F a(n) = (n^2-1)/8 for n>7 and odd.
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>12.
%F G.f.: x*(1-2*x^2+x^3+5*x^4+13*x^5-22*x^6-26*x^7+32*x^8+14*x^9-14*x^10-x^11) / ((1-x)^3*(1+x)^2).
%F (End)
%t LinearRecurrence[{1,2,-2,-1,1},{1,1,1,2,6,21,7,10,10,15,15,21,21},70] (* _Harvey P. Dale_, Sep 18 2019 *)
%o (PARI) Vec(x*(1-2*x^2+x^3+5*x^4+13*x^5-22*x^6-26*x^7+32*x^8+14*x^9-14*x^10-x^11) / ((1-x)^3*(1+x)^2) + O(x^50)) \\ _Colin Barker_, May 27 2016
%Y Cf. A128526, A128527, A128528.
%K nonn,easy
%O 1,4
%A _David Applegate_ and _N. J. A. Sloane_, Mar 05 2007
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