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A120162 a(n) = 3 + floor((2 + Sum_{j=1..n-1} a(j))/4).

%I A120162 #9 Sep 03 2023 08:41:06
%S A120162 3,4,5,6,8,10,12,15,19,24,30,37,46,58,72,90,113,141,176,220,275,344,
%T A120162 430,538,672,840,1050,1313,1641,2051,2564,3205,4006,5008,6260,7825,
%U A120162 9781,12226,15283,19103
%N A120162 a(n) = 3 + floor((2 + Sum_{j=1..n-1} a(j))/4).
%H A120162 G. C. Greubel, <a href="/A120162/b120162.txt">Table of n, a(n) for n = 1..1000</a>
%t A120162 f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q + Sum[f[k,p,q], {k,n-1}], 4];
%t A120162 A120162[n_]:= f[n,3,2];
%t A120162 Table[A120162[n], {n,60}] (* _G. C. Greubel_, Sep 02 2023 *)
%o A120162 (Magma)
%o A120162 function f(n, a, b)
%o A120162   t:=0;
%o A120162     for k in [1..n-1] do
%o A120162       t+:= a+Floor((b+t)/4);
%o A120162     end for;
%o A120162   return t;
%o A120162 end function;
%o A120162 g:= func< n, a, b | f(n+1,a,b)-f(n,a,b) >;
%o A120162 A120162:= func< n | g(n, 3, 2) >;
%o A120162 [A120162(n): n in [1..60]]; // _G. C. Greubel_, Sep 02 2023
%o A120162 (SageMath)
%o A120162 @CachedFunction
%o A120162 def f(n,p,q): return p + (q + sum(f(k,p,q) for k in range(1,n)))//4
%o A120162 def A120162(n): return f(n,3,2)
%o A120162 [A120162(n) for n in range(1,61)] # _G. C. Greubel_, Sep 02 2023
%Y A120162 Cf. A072493, A073941, A112088.
%K A120162 nonn
%O A120162 1,1
%A A120162 _Graeme McRae_, Jun 10 2006
%E A120162 Name edited by _G. C. Greubel_, Sep 02 2023