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A120154 a(n) = 9 + floor( Sum_{j=1..n-1} a(j)/3 ).

%I A120154 #8 Jul 07 2023 05:45:38
%S A120154 9,12,16,21,28,37,50,66,88,118,157,209,279,372,496,661,882,1176,1568,
%T A120154 2090,2787,3716,4955,6606,8808,11744,15659,20879,27838,37118,49490,
%U A120154 65987,87983,117310,156414,208552,278069,370759,494345,659127
%N A120154 a(n) = 9 + floor( Sum_{j=1..n-1} a(j)/3 ).
%H A120154 G. C. Greubel, <a href="/A120154/b120154.txt">Table of n, a(n) for n = 1..1000</a>
%t A120154 A120154[n_]:= A120154[n]= 9 +Quotient[Sum[A120154[k], {k,n-1}], 3];
%t A120154 Table[A120154[n], {n,60}] (* _G. C. Greubel_, Jun 20 2023 *)
%o A120154 (Magma)
%o A120154 function f(n,a,b)
%o A120154   t:=0;
%o A120154     for k in [1..n-1] do
%o A120154        t+:= a+Floor((b+t)/3);
%o A120154      end for;
%o A120154   return t;
%o A120154 end function;
%o A120154 g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
%o A120154 A120154:= func< n | g(n,9,0) >;
%o A120154 [A120154(n): n in [1..60]]; // _G. C. Greubel_, Jun 20 2023
%o A120154 (SageMath)
%o A120154 @CachedFunction
%o A120154 def A120154(n): return 9 + (sum(A120154(k) for k in range(1,n)))//3
%o A120154 [A120154(n) for n in range(1,61)] # _G. C. Greubel_, Jun 20 2023
%Y A120154 Cf. A072493, A073941, A112088.
%K A120154 nonn
%O A120154 1,1
%A A120154 _Graeme McRae_, Jun 10 2006