OFFSET
0,3
COMMENTS
Hankel transform is A168495.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
G.f.: 1/(1-x/(1-x/(1-3x/(1-x/(1-x/(1-3x/(1-x/(1-x/(1-3x/(1-.... (continued fraction);
G.f.: 1/(1-x-x^2/(1-4x-3x^2/(1-2x-3x^2/(1-4x-x^2/(1-4x-3x^2/(1-2x-3x^2/(1-4x-x^2/(1-... (continued fraction),
with sequences (1,3,3,1,3,3,1,3,3,1,...) and (1,4,2,4,4,2,4,4,2,4,4,...).
G.f.: (1+x-sqrt(1-10x+25x^2-12x^3))/(6x(1-x)).
a(n) = Sum_{k=0..n} A091866(n,k)*3^(n-k). - Philippe Del�ham, Nov 27 2009
Conjecture: (n+1)*a(n) +(4-11*n)*a(n-2) +5*(7*n-11)*a(n-2) +(92-37*n) * a(n-3) +6*(2*n-7)*a(n-4) = 0. - R. J. Mathar, Sep 30 2012
a(n) ~ sqrt(33-sqrt(33))*((7+sqrt(33))/2)^n/(12*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012
MATHEMATICA
CoefficientList[Series[(1+x-Sqrt[1-10*x+25*x^2-12*x^3])/(6*x*(1-x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 27 2009
STATUS
approved