OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the single oxide chain SOX(n), defined pictorially in the Simonraj et al. reference (Fig. 4, where SOX(9) is shown, marked as OX(1,9)).
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.
The M-polynomial of SL(n) is M(SL(n); x, y) = 2*x^2*y^2 + 2*n*x^2*y^4 + (n - 2)*x^4*y^4 (n>=2).
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
F. Simonraj and A. George, Topological properties of few poly oxide, poly silicate, DOX and DSL networks, International J. of Future Computer and Communication, 2, No. 2, 2013, 90-95.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
From Colin Barker, May 29 2018: (Start)
G.f.: 4*x*(3 + 2*x) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>2.
(End)
MAPLE
seq(-8+20*n, n = 1 .. 50);
PROG
(GAP) List([1..50], n->20*n-8); # Muniru A Asiru, May 27 2018
(PARI) Vec(4*x*(3 + 2*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 26 2018
STATUS
approved