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A304826
a(n) = 32*7^n/21 - 8/3, n>=1.
4
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 19 2018
STATUS
approved