OFFSET
2,1
COMMENTS
The Lucas cube Lambda(n) can be defined as the graph whose vertices are the binary strings of length n without either two consecutive 1's or a 1 in the first and in the last position, and in which two vertices are adjacent when their Hamming distance is exactly 1.
LINKS
G. G. Cash, Relationship between the Hosoya polynomial and the hyper-Wiener index, Appl. Math. Letters, 15, 2002, 893-895.
S. Klavzar, M. Mollard, Wiener index and Hosoya polynomial of Fibonacci and Lucas cubes, MATCH Commun. Math. Comput. Chem., 68, 2012, 311-324.
E. Munarini, C. P. Cippo, N. Z. Salvi, On the Lucas cubes, The Fibonacci Quarterly, 39, No. 1, 2001, 12-21.
FORMULA
G.f.: z^2(5-18z+24z^2-14z^3+3z^4-z^5)/((1+z)^3*(1-3*z+z^2)^3).
MAPLE
g := z^2*(5-18*z+24*z^2-14*z^3+3*z^4-z^5)/((1+z)^3*(z^2-3*z+1)^3): gser := series(g, z = 0, 40): seq(coeff(gser, z, j), j = 2 .. 35);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 18 2014
STATUS
approved