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A216113 The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 5
42, 477, 2241, 6846, 16380, 33507, 61467, 104076, 165726, 251385, 366597, 517482, 710736, 953631, 1254015, 1620312, 2061522, 2587221, 3207561, 3933270, 4775652, 5746587, 6858531, 8124516, 9558150, 11173617, 12985677, 15009666, 17261496, 19757655 (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^{4n+1}-nt^5+nt-t)/(t^4-1)^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 (5,-10,10,-5,1).

FORMULA

a(n) = 3n(16n^3 + 8n^2 - 5n +9)/2.

G.f.: 3*x*(3*x^3-92*x^2-89*x-14)/(x-1)^5. [Colin Barker, Oct 30 2012]

MAPLE

seq(3*n*(16*n^3+8*n^2-5*n+9)*(1/2), n=1..30);

MATHEMATICA

LinearRecurrence[{5, -10, 10, -5, 1}, {42, 477, 2241, 6846, 16380}, 30] (* Jean-Fran├žois Alcover, Sep 23 2017 *)

CROSSREFS

Cf. A216108-A216112.

Sequence in context: A328175 A216109 A216111 * A204566 A249233 A249234

Adjacent sequences:  A216110 A216111 A216112 * A216114 A216115 A216116

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Oct 26 2012

STATUS

approved

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Last modified December 11 01:07 EST 2019. Contains 329910 sequences. (Running on oeis4.)