%I #42 Aug 09 2024 10:08:26
%S 3,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N a(n) = H_n(1,2) where H_n is the n-th hyperoperator.
%C See A054871 for definitions and key links.
%C Sequence is also the decimal expansion of 2989/9000.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F From _Elmo R. Oliveira_, Jul 16 2024: (Start)
%F G.f.: (3-x^2-x^3)/(1-x).
%F a(n) = 1 for n >= 3. (End)
%F E.g.f.: exp(x) + 2 + 2*x + x^2/2. - _Elmo R. Oliveira_, Aug 09 2024
%e a(0) = H_0(1,2) = 2+1 = 3;
%e a(1) = H_1(1,2) = 1+2 = 3;
%e a(2) = H_2(1,2) = 1*2 = 2;
%e a(3) = H_3(1,2) = 1^2 = 1;
%e a(4) = H_4(1,2) = 1^^2 = 1.
%Y Cf. A054871.
%K nonn,cons,easy
%O 0,1
%A _Natan Arie Consigli_, Aug 24 2015