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A216108 The Wiener index of the ortho-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 5
27, 198, 585, 1260, 2295, 3762, 5733, 8280, 11475, 15390, 20097, 25668, 32175, 39690, 48285, 58032, 69003, 81270, 94905, 109980, 126567, 144738, 164565, 186120, 209475, 234702, 261873, 291060, 322335, 355770 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Hosoya-Wiener polynomial of the graph is n(6+6t+6t^2+3t^3)+(1+2t+2t^2+t^3)^2*(t^{2n+1}-nt^3+nt-t)/(t^2-1)^2.

REFERENCES

Y. Dou, H. Bian, H. Gao, and H. Yu, The polyphenyl chains with extremal edge-Wiener indices, MATCH Commun. Math. Comput. Chem., 64, 2010, 757-766.

LINKS

Table of n, a(n) for n=1..30.

H. Deng,  Wiener indices of spiro and polyphenyl hexagonal chains, arXiv:1006.5488

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 12n^3+36n^2-21n.

G.f.: -9*x*(5*x^2-10*x-3)/(x-1)^4. [Colin Barker, Oct 30 2012]

EXAMPLE

a(1)=27 because we have only 1 hexagon with Wiener index 6*1 + 6*2 + 3*3 = 27.

MAPLE

seq(12*n^3+36*n^2-21*n, n=1..30);

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {27, 198, 585, 1260}, 30] (* Jean-Fran├žois Alcover, Sep 23 2017 *)

CROSSREFS

Cf. A216109, A216110, A216111, A216112, A216113.

Sequence in context: A228463 A000499 A042416 * A216110 A216112 A183596

Adjacent sequences:  A216105 A216106 A216107 * A216109 A216110 A216111

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Oct 26 2012

STATUS

approved

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Last modified May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)