A120161 - OEIS

%I #14 Mar 07 2024 11:13:39

%S 2,2,3,4,5,6,7,9,11,14,18,22,28,35,43,54,68,85,106,132,165,207,258,

%T 323,404,505,631,789,986,1232,1540,1925,2407,3008,3760,4700,5875,7344,

%U 9180,11475,14344,17930,22412,28015,35019,43774,54717,68397,85496,106870

%N a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/4).

%H G. C. Greubel, <a href="/A120161/b120161.txt">Table of n, a(n) for n = 1..1000</a>

%t f[s_]:= Append[s, Floor[(9 +Plus @@ s)/4]]; Nest[f, {2}, 49] (* _Robert G. Wilson v_, Jul 08 2006 *)

%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 A120161:= func< n | g(n,2,1) >;

%o [A120161(n): n in [1..60]]; // _G. C. Greubel_, Sep 02 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 A120161(n): return f(n,2,1)

%o [A120161(n) for n in range(1,61)] # _G. C. Greubel_, Sep 02 2023

%Y Cf. A072493, A073941, A112088.

%K nonn

%O 1,1

%A _Graeme McRae_, Jun 10 2006

%E More terms from _Robert G. Wilson v_, Jul 08 2006

%E Name edited by _G. C. Greubel_, Sep 02 2023