OFFSET
1,3
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n=1..200
F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
FORMULA
G.f.: x + x*U(x) + (1/2)*(3*x-1)*U(x)^2 + (1/2)*(1+x)*U(x^2) + (1/3)*x*U(x)^3 + (2/3)*x*U(x^3), where U(x)=(1-3*x-sqrt(1-6*x+5*x^2))/(2*x). - Emeric Deutsch, May 02 2004
a(n) ~ 5^(n+1/2)/(2*sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, Aug 13 2013
PROG
(PARI) x = 'x+O('x^66);
U(x) = (1-3*x-sqrt(1-6*x+5*x^2))/(2*x);
gf = x + x*U(x) + (1/2)*(3*x-1)*U(x)^2 + (1/2)*(1+x)*U(x^2) + (1/3)*x*U(x)^3 + (2/3)*x*U(x^3);
Vec(gf) \\ Joerg Arndt, Aug 13 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, May 02 2004
STATUS
approved