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A245833 The Szeged index of the triangle-shaped benzenoid T_k (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 (list; graph; refs; listen; history; text; internal format)
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) = (k^6+12k^5+49k^4+84k^3+58k^2+12k)/4.
G.f.: 18z(3+9z-2z^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);
CROSSREFS
Sequence in context: A233364 A222968 A228016 * A254701 A086577 A193152
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 07 2014
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)