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A120169 a(n) = 12 + floor((1 + Sum_{j=1..n-1} a(j))/4).

%I A120169 #8 Sep 10 2023 09:07:33
%S A120169 12,15,19,23,29,36,45,57,71,89,111,139,173,217,271,339,423,529,661,
%T A120169 827,1033,1292,1615,2018,2523,3154,3942,4928,6160,7700,9625,12031,
%U A120169 15039,18798,23498,29372,36715,45894,57368,71710
%N A120169 a(n) = 12 + floor((1 + Sum_{j=1..n-1} a(j))/4).
%H A120169 Harvey P. Dale, <a href="/A120169/b120169.txt">Table of n, a(n) for n = 1..1000</a>
%t A120169 nxt[{t_,a_}]:=Module[{c=Floor[(t+49)/4]},{t+c,c}]; NestList[nxt,{12,12},40][[All,2]] (* _Harvey P. Dale_, Jun 21 2017 *)
%o A120169 (Magma)
%o A120169 function f(n, a, b)
%o A120169   t:=0;
%o A120169     for k in [1..n-1] do
%o A120169       t+:= a+Floor((b+t)/4);
%o A120169     end for;
%o A120169   return t;
%o A120169 end function;
%o A120169 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120169 A120169:= func< n | g(n, 12, 1) >;
%o A120169 [A120169(n): n in [1..60]]; // _G. C. Greubel_, Sep 09 2023
%o A120169 (SageMath)
%o A120169 @CachedFunction
%o A120169 def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
%o A120169 def A120169(n): return f(n, 12, 1)
%o A120169 [A120169(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 09 2023
%Y A120169 Cf. A072493, A073941, A112088.
%Y A120169 Cf. A120149, A120160 - A120168, A120171.
%K A120169 nonn,easy
%O A120169 1,1
%A A120169 _Graeme McRae_, Jun 10 2006