A120169 - OEIS

%I #8 Sep 10 2023 09:07:33

%S 12,15,19,23,29,36,45,57,71,89,111,139,173,217,271,339,423,529,661,

%T 827,1033,1292,1615,2018,2523,3154,3942,4928,6160,7700,9625,12031,

%U 15039,18798,23498,29372,36715,45894,57368,71710

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

%H Harvey P. Dale, <a href="/A120169/b120169.txt">Table of n, a(n) for n = 1..1000</a>

%t 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 (Magma)

%o function f(n, a, b)

%o   t:=0;

%o     for k in [1..n-1] do

%o       t+:= a+Floor((b+t)/4);

%o     end for;

%o   return t;

%o end function;

%o g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;

%o A120169:= func< n | g(n, 12, 1) >;

%o [A120169(n): n in [1..60]]; // _G. C. Greubel_, Sep 09 2023

%o (SageMath)

%o @CachedFunction

%o def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4

%o def A120169(n): return f(n, 12, 1)

%o [A120169(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 09 2023

%Y Cf. A072493, A073941, A112088.

%Y Cf. A120149, A120160 - A120168, A120171.

%K nonn,easy

%O 1,1

%A _Graeme McRae_, Jun 10 2006