OFFSET
1,1
COMMENTS
a(n) (n>=2) is the second 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 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.
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
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
a(n) = A063164(n) for n > 1.
From Colin Barker, May 29 2018: (Start)
G.f.: 8*x*(1 + 3*x) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>2.
(End)
MAPLE
seq(32*n - 24, n = 1 .. 50);
MATHEMATICA
32*Range[60]-24 (* or *) LinearRecurrence[{2, -1}, {8, 40}, 60] (* Harvey P. Dale, Mar 13 2022 *)
PROG
(GAP) List([1..50], n->32*n-24); # Muniru A Asiru, May 27 2018
(PARI) Vec(8*x*(1 + 3*x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 26 2018
STATUS
approved