OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the crystal structure cubic carbon CCC(n), defined in the Baig et al. and in the Gao et al. references.
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
For n>=2 the M-polynomial of the crystal structure cubic carbon CCC(n) is M(CCC(n); x,y) = 72*7^(n-2)*x^3*y^3 + 24*7^(n-2)*x^3*y^4 + (76*7^(n-2) - 16)*x^4*y^4/3.
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.
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
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 21 2018: (Start)
G.f.: 8*x*(9 + 23*x) / ((1 - x)*(1 - 7*x)).
a(n) = 8*a(n-1) - 7*a(n-2) for n>2. (End)
MAPLE
seq((344*7^(n-1)-128)*(1/3), n = 1 .. 25);
MATHEMATICA
LinearRecurrence[{8, -7}, {72, 760}, 30] (* Harvey P. Dale, Aug 24 2019 *)
PROG
(PARI) Vec(8*x*(9 + 23*x) / ((1 - x)*(1 - 7*x)) + O(x^30)) \\ Colin Barker, May 21 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 21 2018
STATUS
approved