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A120159 a(n) = 15 + floor((2 + Sum_{j=1..n-1} a(j))/3).

%I A120159 #9 Jun 27 2025 21:41:54
%S A120159 15,20,27,36,48,64,85,114,152,202,270,360,480,640,853,1137,1516,2022,
%T A120159 2696,3594,4792,6390,8520,11360,15146,20195,26927,35902,47870,63826,
%U A120159 85102,113469,151292,201723,268964,358618,478158,637544,850058,1133411
%N A120159 a(n) = 15 + floor((2 + Sum_{j=1..n-1} a(j))/3).
%H A120159 G. C. Greubel, <a href="/A120159/b120159.txt">Table of n, a(n) for n = 1..1000</a>
%t A120159 A120159[n_]:= A120159[n]= 15 +Quotient[2 +Sum[A120159[k], {k,n-1}], 3];
%t A120159 Table[A120159[n], {n, 60}] (* _G. C. Greubel_, Aug 31 2023 *)
%o A120159 (Magma)
%o A120159 function f(n, a, b)
%o A120159   t:=0;
%o A120159     for k in [1..n-1] do
%o A120159       t+:= a+Floor((b+t)/3);
%o A120159     end for;
%o A120159   return t;
%o A120159 end function;
%o A120159 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120159 A120159:= func< n | g(n, 15, 2) >;
%o A120159 [A120159(n): n in [1..60]]; // _G. C. Greubel_, Aug 31 2023
%o A120159 (SageMath)
%o A120159 @CachedFunction
%o A120159 def A120159(n): return 15 +(2+sum(A120159(k) for k in range(1, n)))//3
%o A120159 [A120159(n) for n in range(1, 61)] # _G. C. Greubel_, Aug 31 2023
%Y A120159 Cf. A072493, A073941, A112088.
%K A120159 nonn,easy
%O A120159 1,1
%A A120159 _Graeme McRae_, Jun 10 2006
%E A120159 Name edited by _G. C. Greubel_, Aug 31 2023