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%I #25 Sep 26 2019 08:07:52
%S 1,7,73,747,7218,65583,567540,4725540,38145600,300244320,2314123992,
%T 17522693064,130682767824,961866429552,6998356983168,50401223526528,
%U 359691525797760,2546051729270400,17889363288835200,124855271993773440,866077921088785152,5974010552957001984,40994676513378284544
%N Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition).
%C For r >= 4, a(r) is the total number of isomers of unbranched alpha-4-catapolynonagons with q = 9 and alpha = 4. Here alpha = 4 is the number of tetragons and r - alpha = r - 4 is the number of q-gons (9-gons) in the alpha-4-catafusene. - _Petros Hadjicostas_, Jul 31 2019
%H J. Brunvoll, S. J. Cyvin, and B. N. Cyvin, <a href="https://doi.org/10.1016/0166-1280(95)04463-9">Isomer enumeration of polygonal systems representing polycyclic conjugated hydrocarbons: unbranched catacondensed systems with tetragons and q-gons</a>, J. Molec. Struct. (Theochem), 364 (1996), 1-13; see Table 12 with q = 9 and alpha = 4.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (30,-342,1620,-108,-27864,77976,86832,-622080,373248,1399680,-1679616).
%F G.f. x^4 +7*x^5 +73*x^6 -9*x^7*(-83 +1688*x -11613*x^2 +15726*x^3 +164862*x^4 -647508*x^5 -283716*x^6 +4642272*x^7 -3888000*x^8 -10101024*x^9 +13576896*x^10) / ( (6*x^2-1)^3*(6*x-1)^5 ). - _R. J. Mathar_, Aug 01 2019
%p # Using the "master formula" in Exhibit 4 (p. 13) with q = 9 and alpha = 4:
%p a := proc(r) 1/4*6^(r - 6)*(36*binomial(r - 2, 2) + 12*binomial(r - 2, 3) + binomial(r - 2, 4)) + 1/4*binomial(2, r - 4) + (1 - 1/2*(-1)^r)*(6*floor(1/2*r) - 6 + binomial(floor(1/2*r) - 1, 2))*6^(floor(1/2*r) - 3); end;
%p seq(a(r), r = 4 .. 30); # _Petros Hadjicostas_, Jul 31 2019
%K nonn,easy
%O 4,2
%A _N. J. A. Sloane_, Aug 13 2006
%E More terms from _Petros Hadjicostas_, Jul 31 2019
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