login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A216108 The Wiener index of the ortho-polyphenyl 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 (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^{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=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^2-21n.

G.f.: -9*x*(5*x^2-10*x-3)/(x-1)^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^2-21*n, n=1..30);

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {27, 198, 585, 1260}, 30] (* Jean-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)