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A120134 a(n) = 4 + floor(Sum_{k=1..n-1} a(k) / 2).

%I A120134 #37 May 13 2023 19:20:29
%S A120134 4,6,9,13,20,30,45,67,101,151,227,340,510,765,1148,1722,2583,3874,
%T A120134 5811,8717,13075,19613,29419,44129,66193,99290,148935,223402,335103,
%U A120134 502655,753982,1130973,1696460,2544690,3817035,5725552,8588328,12882492
%N A120134 a(n) = 4 + floor(Sum_{k=1..n-1} a(k) / 2).
%H A120134 G. C. Greubel, <a href="/A120134/b120134.txt">Table of n, a(n) for n = 1..1000</a>
%F A120134 a(n) ~ c * (3/2)^n, where c = 3.9320886310283094862025842648411406926537121258867950257873967568454133192... - _Vaclav Kotesovec_, May 07 2023
%p A120134 a := proc(n) option remember; 4 + iquo(add(a(k), k = 1..n-1), 2) end:
%p A120134 seq(a(n), n = 1..37); # _Peter Luschny_, May 07 2023
%t A120134 f[s_]:= Append[s, 4+Floor[Plus @@ s/2]]; Nest[f, {4}, 37] (* _Robert G. Wilson v_, Jun 10 2006 *)
%o A120134 (SageMath)
%o A120134 @CachedFunction
%o A120134 def A120134(n): return 4 + sum(A120134(k) for k in range(1,n))//2
%o A120134 print([A120134(n) for n in range(1,41)])  # _G. C. Greubel_, May 07 2023
%Y A120134 Cf. A073941, A072493, A112088, A120135 - A120209, A172161.
%K A120134 nonn
%O A120134 1,1
%A A120134 _Graeme McRae_, Jun 10 2006
%E A120134 Name edited by _Peter Luschny_, May 07 2023