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A120157 a(n) = 13 + floor(Sum_{j=1..n-1} a(j)/3).

%I A120157 #8 Sep 01 2023 04:15:08
%S A120157 13,17,23,30,40,54,72,96,128,170,227,303,404,538,718,957,1276,1701,
%T A120157 2268,3024,4032,5376,7168,9558,12744,16992,22656,30208,40277,53703,
%U A120157 71604,95472,127296,169728,226304,301738,402318,536424,715232,953642
%N A120157 a(n) = 13 + floor(Sum_{j=1..n-1} a(j)/3).
%H A120157 Harvey P. Dale, <a href="/A120157/b120157.txt">Table of n, a(n) for n = 1..1000</a>
%t A120157 Module[{lst={13}},Do[AppendTo[lst,13+Floor[Total[lst]/3]],{40}];lst] (* _Harvey P. Dale_, May 22 2012 *)
%o A120157 (Magma)
%o A120157 function f(n, a, b)
%o A120157   t:=0;
%o A120157     for k in [1..n-1] do
%o A120157       t+:= a+Floor((b+t)/3);
%o A120157     end for;
%o A120157   return t;
%o A120157 end function;
%o A120157 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120157 A120157:= func< n | g(n, 13, 0) >;
%o A120157 [A120157(n): n in [1..60]]; // _G. C. Greubel_, Aug 31 2023
%o A120157 (SageMath)
%o A120157 @CachedFunction
%o A120157 def A120157(n): return 13 +(sum(A120157(k) for k in range(1, n)))//3
%o A120157 [A120157(n) for n in range(1, 61)] # _G. C. Greubel_, Aug 31 2023
%Y A120157 Cf. A072493, A073941, A112088.
%K A120157 nonn
%O A120157 1,1
%A A120157 _Graeme McRae_, Jun 10 2006
%E A120157 Name edited by _G. C. Greubel_, Aug 31 2023