%I #14 Jan 16 2019 17:40:21

%S 1256,9304,65640,459992,3220456,22543704,157806440,1104645592,

%T 7732519656,54127638104,378893467240,2652254271192,18565779898856,

%U 129960459292504,909723215048040,6368062505336792,44576437537358056,312035062761506904,2184245439330548840

%N a(n) = 4024*7^n/147 - 256/3 (n >= 2).

%C a(n) is the second Zagreb index of the crystal structure cubic carbon CCC(n), defined in the Baig et al. and in the Gao et al. references.

%C 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.

%C For n>=2 the M-polynomial of the crystal structure cubic carbon CCC(n) is M(CCC(n); x,y) = 72*7^(n-2)*x^3*y^3 + 24*7^(n-2)*x^3*y^4 + (76*7^(n-2) - 16)*x^4*y^4/3.

%H Colin Barker, <a href="/A304829/b304829.txt">Table of n, a(n) for n = 2..1000</a>

%H A. Q. Baig, M. Imran, W. Khalid, and M. Naeem, <a href="https://doi.org/10.1139/cjc-2017-0083">Molecular description of carbon graphite and crystal cubic carbon structures</a>, Canadian J. Chem., 95, 674-686, 2017.

%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 W. Gao, M. K. Siddiqui, M. Naeem and N. A. Rehman, <a href="https://doi.org/10.3390/molecules22091496">Topological characterization of carbon graphite and crystal cubic carbon structures</a>, Molecules, 22, 1496, 1-12, 2017.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).

%F From _Bruno Berselli_, May 21 2018: (Start)

%F G.f.: 8*x^2*(157 - 93*x)/((1 - x)*(1 - 7*x)).

%F a(n) = 8*a(n-1) - 7*a(n-2) = 7*a(n-1) + 512.

%F a(n) = (8/3)*(503*7^(n-2) - 32). (End)

%p seq((4024*7^(n-2)-256)*(1/3), n = 2 .. 25);

%t Table[4024 7^n/147 - 256/3, {n, 2, 30}] (* _Bruno Berselli_, May 21 2018 *)

%t LinearRecurrence[{8,-7},{1256,9304},30] (* _Harvey P. Dale_, Jan 16 2019 *)

%o (PARI) Vec( 8*x^2*(157 - 93*x)/((1 - x)*(1 - 7*x)) + O(x^40)) \\ _Colin Barker_, May 23 2018

%Y Cf. A304826, A304827, A304828.

%K nonn,easy

%O 2,1

%A _Emeric Deutsch_, May 21 2018