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%I #15 Mar 29 2019 05:02:38
%S 66,144,222,300,378,456,534,612,690,768,846,924,1002,1080,1158,1236,
%T 1314,1392,1470,1548,1626,1704,1782,1860,1938,2016,2094,2172,2250,
%U 2328,2406,2484,2562,2640,2718,2796,2874,2952,3030,3108,3186,3264,3342,3420,3498,3576
%N a(n) = 78*n + 66.
%C a(n) (n>=1) is the first Zagreb index of the triple-layered naphthalenophane G(n,n,n) having n hexagons in each layer. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph. The pictorial definition of G(p,q,r) can be viewed in the E. Flapan references.
%C The M-polynomial of the triple layered naphthalenophane G(p,q,r) is M(G(p,q,r),x,y) = 8*x^2*y^2 + 4*(p + q + r + 2)*x^2*y^3 + (p + q + r - 1)*x^3*y^3 (p, q, r>=1).
%D Erica Flapan, When Topology Meets Chemistry, Cambridge Univ. Press, Cambridge, 2000.
%H E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H Erica Flapan and Brian Forcum, <a href="https://www.researchgate.net/publication/257591558_Intrinsic_Chirality_of_Multipartite_Graphs">Intrinsic chirality of triple-layered naphthalenophane and related graphs</a>, J. Math. Chemistry, 24, 1998, 379-388.
%H I. Gutman and K. C. Das, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match50/match50_83-92.pdf">The first Zagreb index 30 years after</a>, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: 6*(11 + 2*x)/(1 - x)^2.
%F a(n) = 6*A269100(n).
%p seq(78*n+66, n = 0..45);
%Y Cf. A269100, A278127.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, Nov 13 2016
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