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A216109 The hyper-Wiener index of the ortho-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 3
42, 477, 1701, 4254, 8820, 16227, 27447, 43596, 65934, 95865, 134937, 184842, 247416, 324639, 418635, 531672, 666162, 824661, 1009869, 1224630, 1471932, 1754907, 2076831, 2441124, 2851350, 3311217, 3824577, 4395426, 5027904, 5726295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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=0..29.

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = 3*(28+123*n+127*n^2+36*n^3+4*n^4)/2 = 3*(n+1)(4*n^3+32*n^2+95*n+28)/2.

G.f.: -3*(33*x^3-88*x^2+89*x+14)/(x-1)^5. [Colin Barker, Oct 29 2012]

MAPLE

seq(3*n*(4*n^3+20*n^2+43*n-39)*(1/2), n=1..30);

MATHEMATICA

LinearRecurrence[{5, -10, 10, -5, 1}, {42, 477, 1701, 4254, 8820}, 30] (* Jean-Fran├žois Alcover, Sep 23 2017 *)

CROSSREFS

Cf. A216108, A216110-A216113.

Sequence in context: A008387 A088626 A328175 * A216111 A216113 A204566

Adjacent sequences:  A216106 A216107 A216108 * A216110 A216111 A216112

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Oct 26 2012

EXTENSIONS

First formula corrected by Colin Barker, Oct 29 2012

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)