A304827 - OEIS

%I #19 May 22 2018 08:16:44

%S 12,116,844,5940,41612,291316,2039244,14274740,99923212,699462516,

%T 4896237644,34273663540,239915644812,1679409513716,11755866596044,

%U 82291066172340,576037463206412,4032262242444916,28225835697114444,197580849879801140,1383065949158608012,9681461644110256116

%N a(n) = 52*7^n/21 - 16/3 (n>=1).

%C a(n) is the number of edges 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="/A304827/b304827.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.: 4*x*(3 + 5*x) / ((1 - x)*(1 - 7*x)).

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

%F (End)

%p seq(52*7^n*(1/21)-16/3, n = 1..25);

%t Rest@ CoefficientList[Series[4 x (3 + 5 x)/((1 - x) (1 - 7 x)), {x, 0, 22}], x] (* or *)

%t LinearRecurrence[{8, -7}, {12, 116}, 22] (* or *)

%t Array[52*7^#/21 - 16/3 &, 22] (* _Michael De Vlieger_, May 20 2018 *)

%o (PARI) Vec(4*x*(3 + 5*x) / ((1 - x)*(1 - 7*x)) + O(x^30)) \\ _Colin Barker_, May 19 2018

%o (GAP) List([1..30], n->52*7^n/21-16/3); # _Muniru A Asiru_, May 19 2018

%Y Cf. A304826.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 19 2018