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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 19 2018
STATUS
approved