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A120166 a(n) = 8 + floor((2 + Sum_{j=1..n-1} a(j))/4).

%I A120166 #7 Sep 10 2023 09:07:45
%S A120166 8,10,13,16,20,25,31,39,49,61,76,95,119,149,186,232,290,363,454,567,
%T A120166 709,886,1108,1385,1731,2164,2705,3381,4226,5283,6603,8254,10318,
%U A120166 12897,16121,20152,25190,31487,39359,49199
%N A120166 a(n) = 8 + floor((2 + Sum_{j=1..n-1} a(j))/4).
%H A120166 G. C. Greubel, <a href="/A120166/b120166.txt">Table of n, a(n) for n = 1..1000</a>
%t A120166 f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
%t A120166 A120166[n_]:= f[n,8,2];
%t A120166 Table[A120166[n], {n, 60}] (* _G. C. Greubel_, Sep 09 2023 *)
%o A120166 (Magma)
%o A120166 function f(n, a, b)
%o A120166   t:=0;
%o A120166     for k in [1..n-1] do
%o A120166       t+:= a+Floor((b+t)/4);
%o A120166     end for;
%o A120166   return t;
%o A120166 end function;
%o A120166 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120166 A120166:= func< n | g(n, 8, 2) >;
%o A120166 [A120166(n): n in [1..60]]; // _G. C. Greubel_, Sep 09 2023
%o A120166 (SageMath)
%o A120166 @CachedFunction
%o A120166 def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
%o A120166 def A120166(n): return f(n, 8, 2)
%o A120166 [A120166(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 09 2023
%Y A120166 Cf. A072493, A073941, A112088.
%Y A120166 Cf. A120160 - A120165, A120167 - A120169.
%K A120166 nonn,easy
%O A120166 1,1
%A A120166 _Graeme McRae_, Jun 10 2006