%I #16 Sep 10 2023 10:29:15
%S 8,12,18,27,41,61,92,138,207,310,465,698,1047,1570,2355,3533,5299,
%T 7949,11923,17885,26827,40241,60361,90542,135813,203719,305579,458368,
%U 687552,1031328,1546992,2320488,3480732,5221098,7831647,11747471,17621206
%N a(n) = 8 + floor( (1 + Sum_{j=1..n-1} a(j)) / 2).
%H G. C. Greubel, <a href="/A120137/b120137.txt">Table of n, a(n) for n = 1..1000</a>
%t a[n_]:= a[n]= 8 +Floor[(1 +Sum[a[k], {k,n-1}])/2];
%t Table[a[n], {n,60}] (* _G. C. Greubel_, May 08 2023 *)
%t nxt[{t_,a_}]:=Module[{c=8+Floor[(1+t)/2]},{t+c,c}]; NestList[nxt,{8,8},40][[;;,2]] (* _Harvey P. Dale_, Sep 10 2023 *)
%o (SageMath)
%o @CachedFunction
%o def A120137(n): return 8 +(1 +sum(A120137(k) for k in range(1,n)))//2
%o [A120137(n) for n in range(1,60)] # _G. C. Greubel_, May 08 2023
%Y Cf. A073941, A072493, A112088, A120134 - A120136, A120138 - A120209.
%K nonn
%O 1,1
%A _Graeme McRae_, Jun 10 2006