OFFSET
1,1
REFERENCES
M. V. Diudea, I. Gutman, and J. Lorentz, Molecular Topology, Nova Science Publishers, Huntington, NY (2001).
LINKS
I. Gutman and S. Klavzar, An algorithm for the calculation of the Szeged index of benzenoid hydrocarbons, preprint.
I. Gutman and 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, and 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 (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = (n^6+12*n^5+49*n^4+84*n^3+58*n^2+12*n)/4.
G.f.: 18*z*(3+9*z-2*z^2)/(1-z)^7.
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: (1/4)*n^6+3*n^5+(49/4)*n^4+21*n^3+(29/2)*n^2+3*n end proc: seq(a(n), n = 1 .. 30);
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {54, 540, 2610, 8820, 23940, 55944, 117180}, 28] (* Stefano Spezia, Sep 19 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 07 2014
STATUS
approved