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A120168 a(n) = 11 + floor(Sum_{j-1..n-1} a(j)/4).

%I A120168 #7 Sep 10 2023 09:07:37
%S A120168 11,13,17,21,26,33,41,51,64,80,100,125,156,195,244,305,381,476,595,
%T A120168 744,930,1163,1453,1817,2271,2839,3548,4435,5544,6930,8663,10828,
%U A120168 13535,16919,21149,26436,33045,41306,51633,64541
%N A120168 a(n) = 11 + floor(Sum_{j-1..n-1} a(j)/4).
%H A120168 G. C. Greubel, <a href="/A120168/b120168.txt">Table of n, a(n) for n = 1..1000</a>
%t A120168 f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
%t A120168 A120168[n_]:= f[n, 11, 0];
%t A120168 Table[A120168[n], {n, 60}] (* _G. C. Greubel_, Sep 09 2023 *)
%o A120168 (Magma)
%o A120168 function f(n, a, b)
%o A120168   t:=0;
%o A120168     for k in [1..n-1] do
%o A120168       t+:= a+Floor((b+t)/4);
%o A120168     end for;
%o A120168   return t;
%o A120168 end function;
%o A120168 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120168 A120168:= func< n | g(n, 11, 0) >;
%o A120168 [A120168(n): n in [1..60]]; // _G. C. Greubel_, Sep 09 2023
%o A120168 (SageMath)
%o A120168 @CachedFunction
%o A120168 def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
%o A120168 def A120168(n): return f(n, 11, 0)
%o A120168 [A120168(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 09 2023
%Y A120168 Cf. A072493, A073941, A112088.
%Y A120168 Cf. A120160 - A120167, A120169.
%K A120168 nonn,easy
%O A120168 1,1
%A A120168 _Graeme McRae_, Jun 10 2006