A156752 a(n) = floor(Catalan(n+1)/Catalan(n)).

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, 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, 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

Offset: 0

Author

Philippe Deléham, Feb 14 2009

Keywords

• nonn
• easy

Comments

Decimal expansion of 3667/30000. - Elmo R. Oliveira, May 05 2024

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A000108, A010701.

Formula

a(n) = floor(A000108(n+1)/A000108(n)).

G.f.: (1+x+x^4)/(1-x).

a(0)=1, a(1) = a(2) = a(3) = 2, a(n) = 3 for n>3.

E.g.f.: 3*exp(x) - 2 - x - x^2/2 - x^3/6. - Elmo R. Oliveira, Aug 09 2024

a(n) = floor(4^(n/(n+1))). - Aaron J Grech, Aug 30 2024