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A120152 a(n) = 6 + floor((1 + Sum_{j=1..n-1} a(j))/3).

%I A120152 #12 Jul 07 2023 05:45:12
%S A120152 6,8,11,14,19,25,34,45,60,80,107,142,190,253,337,450,600,800,1066,
%T A120152 1422,1896,2528,3370,4494,5992,7989,10652,14203,18937,25249,33666,
%U A120152 44888,59850,79800,106400,141867,189156,252208,336277,448370
%N A120152 a(n) = 6 + floor((1 + Sum_{j=1..n-1} a(j))/3).
%H A120152 G. C. Greubel, <a href="/A120152/b120152.txt">Table of n, a(n) for n = 1..1000</a>
%t A120152 Module[{lista={6}},Do[AppendTo[lista,Floor[(19+Total[lista])/3]],{40}];lista] (* _Harvey P. Dale_, Jun 11 2013 *)
%t A120152 nxt[{s_,a_}]:=Module[{x=Floor[(19+s)/3]},{s+x,x}]; NestList[nxt,{6,6},40][[;;,2]] (* _Harvey P. Dale_, Mar 26 2023 *)
%o A120152 (Magma)
%o A120152 function f(n,a,b)
%o A120152   t:=0;
%o A120152     for k in [1..n-1] do
%o A120152       t+:= a+Floor((b+t)/3);
%o A120152     end for;
%o A120152   return t;
%o A120152 end function;
%o A120152 g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
%o A120152 A120152:= func< n | g(n,6,1) >;
%o A120152 [A120152(n): n in [1..60]]; // _G. C. Greubel_, Jun 15 2023
%o A120152 (SageMath)
%o A120152 @CachedFunction
%o A120152 def A120152(n): return 6 + (1 + sum(A120152(k) for k in range(1,n)))//3
%o A120152 [A120152(n) for n in range(1, 61)] # _G. C. Greubel_, Jun 15 2023
%Y A120152 Cf. A072493, A073941, A112088.
%K A120152 nonn
%O A120152 1,1
%A A120152 _Graeme McRae_, Jun 10 2006