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

1,1

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).

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

Adjacent sequences: A245827 A245828 A245829 * A245831 A245832 A245833

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 07 2014

Status

approved