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A261143 a(n) = H_n(1,2) where H_n is the n-th hyperoperator.

%I A261143 #46 Nov 01 2024 12:41:03
%S A261143 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 A261143 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 A261143 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 A261143 a(n) = H_n(1,2) where H_n is the n-th hyperoperator.
%C A261143 See A054871 for definitions and key links.
%C A261143 Sequence is also the decimal expansion of 2989/9000.
%H A261143 Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, <a href="https://ceur-ws.org/Vol-3792/paper19.pdf">Integer sequences from k-iterated line digraphs</a>, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
%H A261143 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A261143 From _Elmo R. Oliveira_, Jul 16 2024: (Start)
%F A261143 G.f.: (3-x^2-x^3)/(1-x).
%F A261143 a(n) = 1 for n >= 3. (End)
%F A261143 E.g.f.: exp(x) + 2 + 2*x + x^2/2. - _Elmo R. Oliveira_, Aug 09 2024
%e A261143 a(0) = H_0(1,2) = 2+1 = 3;
%e A261143 a(1) = H_1(1,2) = 1+2 = 3;
%e A261143 a(2) = H_2(1,2) = 1*2 = 2;
%e A261143 a(3) = H_3(1,2) = 1^2 = 1;
%e A261143 a(4) = H_4(1,2) = 1^^2 = 1.
%Y A261143 Cf. A054871.
%K A261143 nonn,cons,easy
%O A261143 0,1
%A A261143 _Natan Arie Consigli_, Aug 24 2015