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A245969 The average Wiener index of the set of all fibonacenes with n hexagons. 1
271, 537, 931, 1477, 2199, 3121, 4267, 5661, 7327, 9289, 11571, 14197, 17191, 20577, 24379, 28621, 33327, 38521, 44227, 50469, 57271, 64657, 72651, 81277, 90559, 100521, 111187, 122581, 134727, 147649, 161371, 175917, 191311, 207577, 224739, 242821, 261847, 281841 (list; graph; refs; listen; history; text; internal format)
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

Cf. A005418.

Sequence in context: A086708 A142637 A288881 * A157485 A038655 A108835

Adjacent sequences:  A245966 A245967 A245968 * A245970 A245971 A245972

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Aug 17 2014

STATUS

approved

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Last modified June 19 00:37 EDT 2021. Contains 345125 sequences. (Running on oeis4.)