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A278127 a(n) = 99*n + 71. 1


%S 71,170,269,368,467,566,665,764,863,962,1061,1160,1259,1358,1457,1556,

%T 1655,1754,1853,1952,2051,2150,2249,2348,2447,2546,2645,2744,2843,

%U 2942,3041,3140,3239,3338,3437,3536,3635,3734,3833,3932,4031,4130,4229,4328,4427,4526

%N a(n) = 99*n + 71.

%C a(n) (n>=1) is the second Zagreb index of the triple-layered naphthalenophane G(n,n,n) having n hexagons in each layer. The second Zagreb index of a simple connected graph is the sum of the degree products 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: (71 + 28*x)/(1 - x)^2.

%p seq(99*n+71, n = 0..45);

%Y Cf. A278126.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Nov 13 2016

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