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A245830
The Szeged index of a benzenoid consisting of a linear chain of n hexagons.
1
54, 243, 656, 1381, 2506, 4119, 6308, 9161, 12766, 17211, 22584, 28973, 36466, 45151, 55116, 66449, 79238, 93571, 109536, 127221, 146714, 168103, 191476, 216921, 244526, 274379, 306568, 341181, 378306, 418031
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(n) = (44*n^3 + 72*n^2 + 43*n + 3)/3.
G.f.: z*(54 + 27*z + 8*z^2 - z^3)/(1-z)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Dec 08 2016
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: (44/3)*n^3+24*n^2+(43/3)*n+1 end proc: seq(a(n), n = 1 .. 30);
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {54, 243, 656, 1381}, 100] (* or *) Table[(44*n^3 + 72*n^2 + 43*n + 3)/3, {n, 1, 100}] (* _G, C, Greubel_, Dec 08 2016 *)
PROG
(PARI) Vec(z*(54 + 27*z + 8*z^2 - z^3)/(1-z)^4 + O(x^50)) \\ G. C. Greubel, Dec 08 2016
CROSSREFS
Cf. A143938.
Sequence in context: A124007 A221867 A248209 * A102838 A090832 A232511
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Aug 07 2014
STATUS
approved