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A245833
The Szeged index of the triangle-shaped benzenoid T_n (see Fig. 5.7 of the Diudea et al. reference).
0
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 07 2014
STATUS
approved