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A120156 a(n) = 11 + floor((2 + Sum_{j=1..n-1} a(j))/3).

%I A120156 #10 Sep 01 2023 02:18:59
%S A120156 11,15,20,27,36,48,64,85,113,151,201,268,358,477,636,848,1131,1508,
%T A120156 2010,2680,3574,4765,6353,8471,11295,15060,20080,26773,35697,47596,
%U A120156 63462,84616,112821,150428,200571,267428,356570,475427,633903,845204
%N A120156 a(n) = 11 + floor((2 + Sum_{j=1..n-1} a(j))/3).
%H A120156 G. C. Greubel, <a href="/A120156/b120156.txt">Table of n, a(n) for n = 1..1000</a>
%t A120156 A120156[n_]:= A120156[n]= 11 +Quotient[2+Sum[A120156[k], {k,n-1}], 3];
%t A120156 Table[A120156[n], {n,60}] (* _G. C. Greubel_, Jul 06 2023 *)
%o A120156 (Magma)
%o A120156 function f(n, a, b)
%o A120156   t:=0;
%o A120156     for k in [1..n-1] do
%o A120156       t+:= a+Floor((b+t)/3);
%o A120156     end for;
%o A120156   return t;
%o A120156 end function;
%o A120156 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120156 A120156:= func< n | g(n, 11, 2) >;
%o A120156 [A120156(n): n in [1..60]]; // _G. C. Greubel_, Jul 06 2023
%o A120156 (SageMath)
%o A120156 @CachedFunction
%o A120156 def A120156(n): return 11 +(2+sum(A120156(k) for k in range(1, n)))//3
%o A120156 [A120156(n) for n in range(1, 61)] # _G. C. Greubel_, Jul 06 2023
%Y A120156 Cf. A072493, A073941, A112088.
%K A120156 nonn
%O A120156 1,1
%A A120156 _Graeme McRae_, Jun 10 2006