%I #19 Aug 30 2024 18:09:28
%S 1,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
%U 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3
%N a(n) = floor(Catalan(n+1)/Catalan(n)).
%C Decimal expansion of 3667/30000. - _Elmo R. Oliveira_, May 05 2024
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F a(n) = floor(A000108(n+1)/A000108(n)).
%F G.f.: (1+x+x^4)/(1-x).
%F a(0)=1, a(1) = a(2) = a(3) = 2, a(n) = 3 for n>3.
%F E.g.f.: 3*exp(x) - 2 - x - x^2/2 - x^3/6. - _Elmo R. Oliveira_, Aug 09 2024
%F a(n) = floor(4^(n/(n+1))). - _Aaron J Grech_, Aug 30 2024
%Y Cf. A000108, A010701.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Feb 14 2009