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A304826 a(n) = 32*7^n/21 - 8/3, n>=1. 4

%I

%S 8,72,520,3656,25608,179272,1254920,8784456,61491208,430438472,

%T 3013069320,21091485256,147640396808,1033482777672,7234379443720,

%U 50640656106056,354484592742408,2481392149196872,17369745044378120,121588215310646856,851117507174528008,5957822550221696072

%N a(n) = 32*7^n/21 - 8/3, n>=1.

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

%H Colin Barker, <a href="/A304826/b304826.txt">Table of n, a(n) for n = 1..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 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 _Colin Barker_, May 19 2018: (Start)

%F G.f.: 8*x*(1 + x) / ((1 - x)*(1 - 7*x)).

%F a(n) = 8*a(n-1) - 7*a(n-2) for n>2.

%F (End)

%p seq(32*7^n*(1/21)-8/3, n = 1 .. 25);

%t Rest@ CoefficientList[Series[8 x (1 + x)/((1 - x) (1 - 7 x)), {x, 0, 22}], x] (* or *)

%t LinearRecurrence[{8, -7}, {8, 72}, 22] (* or *)

%t Array[32*7^#/21 - 8/3 &, 22] (* _Michael De Vlieger_, May 20 2018 *)

%o (PARI) Vec(8*x*(1 + x) / ((1 - x)*(1 - 7*x)) + O(x^30)) \\ _Colin Barker_, May 19 2018

%o (GAP) List([1..30], n->32*7^n/21-8/3); # _Muniru A Asiru_, May 19 2018

%Y Cf. A304827.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 19 2018

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Last modified August 18 22:08 EDT 2019. Contains 326109 sequences. (Running on oeis4.)