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A120153 a(n) = 7 + floor((2 + Sum_{j=1..n-1} a(j))/3).

%I A120153 #10 Jun 16 2023 11:37:24
%S A120153 7,10,13,17,23,31,41,55,73,97,130,173,231,308,410,547,729,972,1296,
%T A120153 1728,2304,3072,4096,5462,7282,9710,12946,17262,23016,30688,40917,
%U A120153 54556,72741,96988,129318,172424,229898,306531,408708,544944
%N A120153 a(n) = 7 + floor((2 + Sum_{j=1..n-1} a(j))/3).
%H A120153 G. C. Greubel, <a href="/A120153/b120153.txt">Table of n, a(n) for n = 1..1000</a>
%t A120153 nxt[{t_,a_}]:=Module[{c=Floor[(23+t)/3]},{t+c,c}]; Rest[Transpose[ NestList[ nxt,{0,7},40]][[2]]] (* _Harvey P. Dale_, Oct 08 2015 *)
%o A120153 (Magma)
%o A120153 function f(n,a,b)
%o A120153   t:=0;
%o A120153     for k in [1..n-1] do
%o A120153       t+:= a+Floor((b+t)/3);
%o A120153     end for;
%o A120153   return t;
%o A120153 end function;
%o A120153 g:= func< n,a,b | f(n+1,a,b)-f(n,a,b) >;
%o A120153 A120153:= func< n | g(n,7,2) >;
%o A120153 [A120153(n): n in [1..60]]; // _G. C. Greubel_, Jun 15 2023
%o A120153 (SageMath)
%o A120153 @CachedFunction
%o A120153 def A120153(n): return 7 + (2 + sum(A120153(k) for k in range(1,n)))//3
%o A120153 [A120153(n) for n in range(1,61)] # _G. C. Greubel_, Jun 15 2023
%Y A120153 Cf. A072493, A073941, A112088.
%K A120153 nonn
%O A120153 1,1
%A A120153 _Graeme McRae_, Jun 10 2006