|
|
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
|
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|