OFFSET
1,1
REFERENCES
M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science Publishers, Huntington, NY (2001).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
I. Gutman, S. Klavzar, An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons, preprint.
I. Gutman, S. Klavzar, An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons, J. Chem. Inf. Comput. Sci., 35, 1995, 1011-1014.
I. Gutman, P. V. Khadikar, T. Khaddar, Wiener and Szeged indices of benzenoid hydrocarbons containing a linear polyacene fragment, Commun. Math. Chem. (MATCH), 35, 1997, 105-116.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (44*n^3 + 72*n^2 + 43*n + 3)/3.
G.f.: z*(54 + 27*z + 8*z^2 - z^3)/(1-z)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Dec 08 2016
EXAMPLE
a(1)=54; indeed, the benzenoid consists of 1 hexagon and each of its six edges contributes 3*3 towards the Szeged index; 6*9 = 54.
MAPLE
a := proc (n) options operator, arrow: (44/3)*n^3+24*n^2+(43/3)*n+1 end proc: seq(a(n), n = 1 .. 30);
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {54, 243, 656, 1381}, 100] (* or *) Table[(44*n^3 + 72*n^2 + 43*n + 3)/3, {n, 1, 100}] (* _G, C, Greubel_, Dec 08 2016 *)
PROG
(PARI) Vec(z*(54 + 27*z + 8*z^2 - z^3)/(1-z)^4 + O(x^50)) \\ G. C. Greubel, Dec 08 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 07 2014
STATUS
approved