OFFSET
3,1
COMMENTS
For the definition of a fibonacene see the Gutman-Klavzar reference.
The number of fibonacenes with n hexagons is A005418(n-2).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 3..1000
A. A. Dobrynin, I. Gutman, The average Wiener index of hexagonal chains, Computers & Chemistry, 23, 1999, 571-576.
I. Gutman, S. Klavžar, Chemical graph theory of fibonacenes, Commun. Math. Chem. (MATCH), 55, 2006, 39-54.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 4n^3 + 16n^2 + 6n + 1 (n>=3) (see p. 45 of the Gutman-Klavzar reference).
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Colin Barker, Aug 31 2014
G.f.: -x^3*(109*x^3-409*x^2+547*x-271) / (x-1)^4. - Colin Barker, Aug 31 2014
EXAMPLE
a(5)=931. Indeed, there are A005418(3)=3 fibonacenes with 5 hexagons (see Fig. 1 of the Gutman-Klavzar reference); their Wiener indices are 963, 931, and 899; average is 931.
MAPLE
seq(4*n^3+16*n^2+6*n+1, n = 3 .. 40);
MATHEMATICA
Table[4 n^3 + 16 n^2 + 6 n + 1, {n, 3, 40}] (* Vincenzo Librandi, Aug 31 2014 *)
PROG
(PARI) Vec(-x^3*(109*x^3-409*x^2+547*x-271)/(x-1)^4 + O(x^100)) \\ Colin Barker, Aug 31 2014
(Magma) [4*n^3 + 16*n^2 + 6*n + 1: n in [3..50]]; // Vincenzo Librandi, Aug 31 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 17 2014
STATUS
approved