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A216112 The Wiener index of the para-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 3
27, 198, 657, 1548, 3015, 5202, 8253, 12312, 17523, 24030, 31977, 41508, 52767, 65898, 81045, 98352, 117963, 140022, 164673, 192060, 222327, 255618, 292077, 331848, 375075, 421902, 472473, 526932, 585423, 648090 (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 (4,-6,4,-1).

FORMULA

a(n) = 3n(1+8n^2).

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

EXAMPLE

a(1)=27 because the graph consists of 1 hexagon and its Wiener index is 6*1+6*2+3*3=27.

MAPLE

seq(24*n^3+3*n, n=1..30);

CROSSREFS

Cf. A216108-A216113.

Sequence in context: A042416 A216108 A216110 * A183596 A033544 A224874

Adjacent sequences:  A216109 A216110 A216111 * A216113 A216114 A216115

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Oct 26 2012

STATUS

approved

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)