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A245832
The Szeged index of the parallelogram-shaped benzenoid Q_k (see Fig. 5.7 of the Diudea et al. reference).
0
54, 1008, 6656, 27340, 84990, 219604, 497168, 1019016, 1932630, 3443880, 5830704, 9458228, 14795326, 22432620, 33101920, 47697104, 67296438, 93186336, 126886560, 170176860, 225125054, 294116548, 379885296, 485546200, 614628950, 771113304, 959465808, 1184677956
OFFSET
1,1
REFERENCES
M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science Publishers, Huntington, NY (2001).
LINKS
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.
FORMULA
a(k) = (12k^6+72k^5+137k^92k^3+13k^2-2k)/6.
G.f: 2z(27+315z+367z^2+13z^3-2z^4)/(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: 2*n^6+12*n^5+(137/6)*n^4+(46/3)*n^3+(13/6)*n^2-(1/3)*n end proc: seq(a(n), n = 1 .. 30);
CROSSREFS
Sequence in context: A160345 A324952 A298718 * A121625 A341940 A190399
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 07 2014
STATUS
approved