OFFSET
3,1
COMMENTS
a(3), a(4), ... , a(16) have been checked by the direct computation of the Wiener index (using Maple).
REFERENCES
Y. Alizadeh, S. Klavzar, The Wiener dimension of a graph (unpublished manuscript).
LINKS
G. Cash, S. Klavzar, M. Petkovsek, Three methods for calculation of the hyper-Wiener index of a molecular graph, J. Chem. Inf. Comput. Sci. 42, 2002, 571-576.
FORMULA
a(n) = 9n(n^2+4n-4).
G.f.: 9z^3(51-92z+63z^2-16z^3)/(1-z)^4.
The Hosoya polynomial of the cyclic phenylene with n hexagons is [n*t^n*(t^5+3t^4+5t^3+5t^2+3t+1) - n(t^8+t^7+t^6+t^5+2t^3+4t^2+8t)]/(t-1).
MAPLE
a := proc (n) options operator, arrow: 9*n*(n^2+4*n-4) end proc: seq(a(n), n = 3 .. 40);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Apr 14 2013
STATUS
approved