A245830 The Szeged index of a benzenoid consisting of a linear chain of n hexagons.

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

Author

Emeric Deutsch, Aug 07 2014

Keywords

• nonn
• easy

Examples

			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.
		

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• 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.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A143938.

Programs

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 *)

PARI

Vec(z*(54 + 27*z + 8*z^2 - z^3)/(1-z)^4 + O(x^50)) \\ G. C. Greubel, Dec 08 2016

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