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A120155 a(n) = 10 + floor( (1 + Sum_{j=1..n-1} a(j) )/3 ).

%I A120155 #6 Jul 07 2023 05:45:54
%S A120155 10,13,18,24,32,42,56,75,100,133,178,237,316,421,562,749,999,1332,
%T A120155 1776,2368,3157,4209,5612,7483,9977,13303,17737,23650,31533,42044,
%U A120155 56059,74745,99660,132880,177173,236231,314975,419966,559955,746607
%N A120155 a(n) = 10 + floor( (1 + Sum_{j=1..n-1} a(j) )/3 ).
%H A120155 G. C. Greubel, <a href="/A120155/b120155.txt">Table of n, a(n) for n = 1..1000</a>
%t A120155 A120155[n_]:= A120155[n]= 10 +Quotient[1 +Sum[A120155[k], {k,n-1}], 3];
%t A120155 Table[A120155[n], {n,60}] (* _G. C. Greubel_, Jun 20 2023 *)
%o A120155 (Magma)
%o A120155 function f(n,a,b)
%o A120155   t:=0;
%o A120155     for k in [1..n-1] do
%o A120155        t+:= a+Floor((b+t)/3);
%o A120155      end for;
%o A120155   return t;
%o A120155 end function;
%o A120155 g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
%o A120155 A120155:= func< n | g(n,10,1) >;
%o A120155 [A120155(n): n in [1..60]]; // _G. C. Greubel_, Jun 20 2023
%o A120155 (SageMath)
%o A120155 @CachedFunction
%o A120155 def A120155(n): return 10 +(1+sum(A120155(k) for k in range(1,n)))//3
%o A120155 [A120155(n) for n in range(1,61)] # _G. C. Greubel_, Jun 20 2023
%Y A120155 Cf. A072493, A073941, A112088.
%K A120155 nonn
%O A120155 1,1
%A A120155 _Graeme McRae_, Jun 10 2006