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%I #21 May 30 2022 13:01:16
%S 1,6,15,34,61,106,162,246,342,477,626,825,1039,1314,1606,1970,2352,
%T 2817,3302,3881,4481,5186,5914,6758,7626,8621,9642,10801,11987,13322,
%U 14686,16210,17764,19489,21246,23185,25157,27322,29522,31926,34366,37021,39714,42633,45591,48786
%N Numbers of graphs which are double triangle descendants of K_5 with four more vertices than triangles.
%C See Laradji, Mishna, Yeats paper for definition of double triangle descendants.
%H Mohamed Laradji, Marni Mishna, and Karen Yeats, <a href="https://arxiv.org/abs/1904.06923">Some results on double triangle descendants of K_5</a>, arXiv:1904.06923 [math.CO], 2019.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,-2,0,2,-1).
%F G.f.: x^9*(1 + 4*x + 3*x^2 + 6*x^3 + 3*x^4 + 4*x^5 + 4*x^7 - 3*x^8 + 3*x^9 - x^10 + x^11)/((1 - x)^4*(1 + x)^2*(1 + x^2)). See Laradji, Mishna, Yeats paper for proof.
%Y Double triangle descendants of K_5 with three more vertices than triangles is A007980. Double triangle descendants of K_5 with two more vertices than triangles is A008619. Double triangle descendants of K_5 with one more vertex than triangles is A000007. Double triangle descendants of K_5 with the same number of vertices as triangles is A000012.
%K nonn,easy
%O 9,2
%A _Karen A. Yeats_, Feb 21 2020