A304827 a(n) = 52*7^n/21 - 16/3 (n>=1).

12, 116, 844, 5940, 41612, 291316, 2039244, 14274740, 99923212, 699462516, 4896237644, 34273663540, 239915644812, 1679409513716, 11755866596044, 82291066172340, 576037463206412, 4032262242444916, 28225835697114444, 197580849879801140, 1383065949158608012, 9681461644110256116

Offset

1,1

Comments

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.

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.: 4*x*(3 + 5*x) / ((1 - x)*(1 - 7*x)).

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

(End)

Maple

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

Mathematica

Rest@ CoefficientList[Series[4 x (3 + 5 x)/((1 - x) (1 - 7 x)), {x, 0, 22}], x] (* or *)
LinearRecurrence[{8, -7}, {12, 116}, 22] (* or *)
Array[52*7^#/21 - 16/3 &, 22] (* Michael De Vlieger, May 20 2018 *)

Prog

(PARI) Vec(4*x*(3 + 5*x) / ((1 - x)*(1 - 7*x)) + O(x^30)) \\ Colin Barker, May 19 2018
(GAP) List([1..30], n->52*7^n/21-16/3); # Muniru A Asiru, May 19 2018

Crossrefs

Cf. A304826.

Sequence in context: A166777 A027285 A238930 * A182671 A154346 A016142

Adjacent sequences: A304824 A304825 A304826 * A304828 A304829 A304830

Keyword

nonn,easy

Author

Emeric Deutsch, May 19 2018

Status

approved