OFFSET
1,1
COMMENTS
a(2) and a(5) have been checked by the direct computation of the Wiener index (using Maple).
REFERENCES
I. Gutman, The topological indices of linear phenylenes, J. Serb. Chem. Soc., 60, No. 2, 1995, 99-104.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
G. Cash, S. Klavzar, M. Petkovsek, Three methods for calculation of the hyper-Wiener index of a molecular graph, J. Chem. Inf. Comput. Sci. 42, 2002, 571-576.
L. Pavlovic, I. Gutman, Wiener numbers of phenylenes: an exact result, J. Chem. Inf. Comput. Sci. 37, 1997, 355-358.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1)
FORMULA
a(n) = 9*n^2*(2n+1) = 9*A099721(n).
G.f.: 9*x*(3 + 8*x + x^2)/(1-x)^4.
The Hosoya polynomial of the linear phenylene with n hexagons is nt(t^3-t^2-4t-8)/(t-1) + 2t(t+1)(t^(3n)-1)/(t-1)^2.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Dec 08 2016
MAPLE
a := proc (n) options operator, arrow: 9*n^2*(2*n+1) end proc: seq(a(n), n = 1 .. 40);
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {27, 180, 567, 1296}, 100] (* or *) Table[9*n^2*(2*n+1), {n, 1, 100}] (* G. C. Greubel, Dec 08 2016 *)
PROG
(PARI) Vec(9*x*(3 + 8*x + x^2)/(1-x)^4 + O(x^50)) \\ G. C. Greubel, Dec 08 2016
(Magma) [9*n^2*(2*n+1): n in [1..40]]; // Vincenzo Librandi, Dec 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 10 2013
STATUS
approved