A245833 The Szeged index of the triangle-shaped benzenoid T_n (see Fig. 5.7 of the Diudea et al. reference).

54, 540, 2610, 8820, 23940, 55944, 117180, 225720, 406890, 694980, 1135134, 1785420, 2719080, 4026960, 5820120, 8232624, 11424510, 15584940, 20935530, 27733860, 36277164, 46906200, 60009300, 76026600, 95454450, 118850004, 146835990, 180105660

Offset

1,1

References

M. V. Diudea, I. Gutman, and J. Lorentz, Molecular Topology, Nova Science Publishers, Huntington, NY (2001).

Links

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

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

Sequence in context: A233364 A222968 A228016 * A254701 A376260 A086577

Adjacent sequences: A245830 A245831 A245832 * A245834 A245835 A245836

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 07 2014

Status

approved