OFFSET
2,1
COMMENTS
a(n) is the second Zagreb index of the crystal structure cubic carbon CCC(n), defined in the Baig et al. and in the Gao et al. references.
The second Zagreb index of a simple connected graph is the sum of the degree products 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 = 2..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 Bruno Berselli, May 21 2018: (Start)
G.f.: 8*x^2*(157 - 93*x)/((1 - x)*(1 - 7*x)).
a(n) = 8*a(n-1) - 7*a(n-2) = 7*a(n-1) + 512.
a(n) = (8/3)*(503*7^(n-2) - 32). (End)
MAPLE
seq((4024*7^(n-2)-256)*(1/3), n = 2 .. 25);
MATHEMATICA
Table[4024 7^n/147 - 256/3, {n, 2, 30}] (* Bruno Berselli, May 21 2018 *)
LinearRecurrence[{8, -7}, {1256, 9304}, 30] (* Harvey P. Dale, Jan 16 2019 *)
PROG
(PARI) Vec( 8*x^2*(157 - 93*x)/((1 - x)*(1 - 7*x)) + O(x^40)) \\ Colin Barker, May 23 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 21 2018
STATUS
approved