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A216110 The Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references). 3
27, 198, 621, 1404, 2655, 4482, 6993, 10296, 14499, 19710, 26037, 33588, 42471, 52794, 64665, 78192, 93483, 110646, 129789, 151020, 174447, 200178, 228321, 258984, 292275, 328302, 367173, 408996, 453879, 501930 (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^{3n+1}-nt^4+nt-t)/(t^3-1)^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) = 18n^3 + 18n^2 -9n.

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

EXAMPLE

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

MAPLE

seq(18*n^3+18*n^2-9*n, n=1..30);

CROSSREFS

Cf. A216108, A216109, A216111-A216113.

Sequence in context: A000499 A042416 A216108 * A216112 A183596 A033544

Adjacent sequences:  A216107 A216108 A216109 * A216111 A216112 A216113

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Oct 26 2012

STATUS

approved

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Last modified November 19 20:42 EST 2019. Contains 329323 sequences. (Running on oeis4.)