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a(n) = floor(Catalan(n+1)/Catalan(n)).
1

%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