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A120158 a(n) = 14 + floor((1 + Sum_{j=1..n-1} a(j))/3).

%I A120158 #10 Sep 01 2023 02:19:06
%S A120158 14,19,25,33,44,59,79,105,140,187,249,332,443,590,787,1049,1399,1865,
%T A120158 2487,3316,4421,5895,7860,10480,13973,18631,24841,33122,44162,58883,
%U A120158 78511,104681,139575,186100,248133,330844,441125,588167,784223,1045630
%N A120158 a(n) = 14 + floor((1 + Sum_{j=1..n-1} a(j))/3).
%H A120158 Harvey P. Dale, <a href="/A120158/b120158.txt">Table of n, a(n) for n = 1..1000</a>
%t A120158 nxt[{a_,t_}]:=Module[{c=Floor[(43+t)/3]},{c,t+c}]; Rest[Transpose[ NestList[ nxt,{14,0},40]][[1]]] (* _Harvey P. Dale_, Jun 12 2014 *)
%t A120158 A120158[n_]:= A120158[n]= 14 +Quotient[1 +Sum[A120158[k], {k,n-1}], 3];
%t A120158 Table[A120158[n], {n, 60}] (* _G. C. Greubel_, Aug 31 2023 *)
%o A120158 (Magma)
%o A120158 function f(n, a, b)
%o A120158   t:=0;
%o A120158     for k in [1..n-1] do
%o A120158       t+:= a+Floor((b+t)/3);
%o A120158     end for;
%o A120158   return t;
%o A120158 end function;
%o A120158 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120158 A120158:= func< n | g(n, 14, 1) >;
%o A120158 [A120158(n): n in [1..60]]; // _G. C. Greubel_, Aug 31 2023
%o A120158 (SageMath)
%o A120158 @CachedFunction
%o A120158 def A120158(n): return 14 +(1+sum(A120158(k) for k in range(1, n)))//3
%o A120158 [A120158(n) for n in range(1, 61)] # _G. C. Greubel_, Aug 31 2023
%Y A120158 Cf. A072493, A073941, A112088.
%K A120158 nonn
%O A120158 1,1
%A A120158 _Graeme McRae_, Jun 10 2006