A120167 - OEIS

%I #10 Sep 10 2023 09:07:41

%S 9,12,15,18,23,29,36,45,56,70,88,110,137,171,214,268,335,418,523,654,

%T 817,1021,1277,1596,1995,2494,3117,3896,4870,6088,7610,9512,11890,

%U 14863,18579,23223,29029,36286,45358,56697

%N a(n) = 9 + floor((3 + Sum_{j=1..n-1} a(j))/4).

%H Harvey P. Dale, <a href="/A120167/b120167.txt">Table of n, a(n) for n = 1..1000</a>

%t nxt[{t_,a_}]:=Module[{c=Floor[(39+t)/4]},{t+c,c}]; NestList[nxt,{9,9},40][[All,2]] (* _Harvey P. Dale_, Apr 24 2019 *)

%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 A120167:= func< n | g(n, 9, 3) >;

%o [A120167(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 A120167(n): return f(n, 9, 3)

%o [A120167(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 09 2023

%Y Cf. A072493, A073941, A112088.

%Y Cf. A120160 - A120166, A120168, A120169.

%K nonn,easy

%O 1,1

%A _Graeme McRae_, Jun 10 2006