A245832 The Szeged index of the parallelogram-shaped benzenoid Q_k (see Fig. 5.7 of the Diudea et al. reference).

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

Table of n, a(n) for n=1..28.

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.

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

Adjacent sequences: A245829 A245830 A245831 * A245833 A245834 A245835

Keyword

nonn

Author

Emeric Deutsch, Aug 07 2014

Status

approved