

A216108


The Wiener index of the orthopolyphenyl 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
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OFFSET

1,1


COMMENTS

The HosoyaWiener polynomial of the graph is n(6+6t+6t^2+3t^3)+(1+2t+2t^2+t^3)^2*(t^{2n+1}nt^3+ntt)/(t^21)^2.


REFERENCES

Y. Dou, H. Bian, H. Gao, and H. Yu, The polyphenyl chains with extremal edgeWiener indices, MATCH Commun. Math. Comput. Chem., 64, 2010, 757766.


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^221n.
G.f.: 9*x*(5*x^210*x3)/(x1)^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^221*n, n=1..30);


MATHEMATICA

LinearRecurrence[{4, 6, 4, 1}, {27, 198, 585, 1260}, 30] (* JeanFrançois 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



