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A120161 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/4).

%I A120161 #14 Mar 07 2024 11:13:39
%S A120161 2,2,3,4,5,6,7,9,11,14,18,22,28,35,43,54,68,85,106,132,165,207,258,
%T A120161 323,404,505,631,789,986,1232,1540,1925,2407,3008,3760,4700,5875,7344,
%U A120161 9180,11475,14344,17930,22412,28015,35019,43774,54717,68397,85496,106870
%N A120161 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/4).
%H A120161 G. C. Greubel, <a href="/A120161/b120161.txt">Table of n, a(n) for n = 1..1000</a>
%t A120161 f[s_]:= Append[s, Floor[(9 +Plus @@ s)/4]]; Nest[f, {2}, 49] (* _Robert G. Wilson v_, Jul 08 2006 *)
%o A120161 (Magma)
%o A120161 function f(n, a, b)
%o A120161   t:=0;
%o A120161     for k in [1..n-1] do
%o A120161       t+:= a+Floor((b+t)/4);
%o A120161     end for;
%o A120161   return t;
%o A120161 end function;
%o A120161 g:= func< n, a, b | f(n+1,a,b)-f(n,a,b) >;
%o A120161 A120161:= func< n | g(n,2,1) >;
%o A120161 [A120161(n): n in [1..60]]; // _G. C. Greubel_, Sep 02 2023
%o A120161 (SageMath)
%o A120161 @CachedFunction
%o A120161 def f(n,p,q): return p + (q + sum(f(k,p,q) for k in range(1,n)))//4
%o A120161 def A120161(n): return f(n,2,1)
%o A120161 [A120161(n) for n in range(1,61)] # _G. C. Greubel_, Sep 02 2023
%Y A120161 Cf. A072493, A073941, A112088.
%K A120161 nonn
%O A120161 1,1
%A A120161 _Graeme McRae_, Jun 10 2006
%E A120161 More terms from _Robert G. Wilson v_, Jul 08 2006
%E A120161 Name edited by _G. C. Greubel_, Sep 02 2023