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

8, 72, 520, 3656, 25608, 179272, 1254920, 8784456, 61491208, 430438472, 3013069320, 21091485256, 147640396808, 1033482777672, 7234379443720, 50640656106056, 354484592742408, 2481392149196872, 17369745044378120, 121588215310646856, 851117507174528008, 5957822550221696072

Offset

1,1

Comments

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.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

A. Q. Baig, M. Imran, W. Khalid, and M. Naeem, Molecular description of carbon graphite and crystal cubic carbon structures, Canadian J. Chem., 95, 674-686, 2017.

W. Gao, M. K. Siddiqui, M. Naeem and N. A. Rehman, Topological characterization of carbon graphite and crystal cubic carbon structures, Molecules, 22, 1496, 1-12, 2017.

Index entries for linear recurrences with constant coefficients, signature (8,-7).

Formula

From Colin Barker, May 19 2018: (Start)

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

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

(End)

Maple

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

Mathematica

Rest@ CoefficientList[Series[8 x (1 + x)/((1 - x) (1 - 7 x)), {x, 0, 22}], x] (* or *)
LinearRecurrence[{8, -7}, {8, 72}, 22] (* or *)
Array[32*7^#/21 - 8/3 &, 22] (* Michael De Vlieger, May 20 2018 *)

Prog

(PARI) Vec(8*x*(1 + x) / ((1 - x)*(1 - 7*x)) + O(x^30)) \\ Colin Barker, May 19 2018
(GAP) List([1..30], n->32*7^n/21-8/3); # Muniru A Asiru, May 19 2018

Crossrefs

Cf. A304827.

Sequence in context: A271028 A180288 A082141 * A270241 A054615 A344067

Adjacent sequences: A304823 A304824 A304825 * A304827 A304828 A304829

Keyword

nonn,easy

Author

Emeric Deutsch, May 19 2018

Status

approved