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
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Oct 26 2012
STATUS
approved