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A120163 a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/4).

%I A120163 #10 Sep 06 2023 01:39:19
%S A120163 4,5,7,8,10,13,16,20,25,31,39,49,61,76,95,119,149,186,233,291,364,455,
%T A120163 568,710,888,1110,1387,1734,2168,2710,3387,4234,5292,6615,8269,10336,
%U A120163 12920,16150,20188,25235
%N A120163 a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/4).
%H A120163 G. C. Greubel, <a href="/A120163/b120163.txt">Table of n, a(n) for n = 1..1000</a>
%t A120163 l={4};Do[l=AppendTo[l,Floor[(19+Total[l])/4]],{40}];l (* _Harvey P. Dale_, Sep 23 2011 *)
%o A120163 (Magma)
%o A120163 function f(n, a, b)
%o A120163   t:=0;
%o A120163     for k in [1..n-1] do
%o A120163       t+:= a+Floor((b+t)/4);
%o A120163     end for;
%o A120163   return t;
%o A120163 end function;
%o A120163 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120163 A120163:= func< n | g(n, 4, 3) >;
%o A120163 [A120163(n): n in [1..60]]; // _G. C. Greubel_, Sep 05 2023
%o A120163 (SageMath)
%o A120163 @CachedFunction
%o A120163 def f(n, p, q): return p + (q + sum(f(k, p, q) for k in range(1, n)))//4
%o A120163 def A120163(n): return f(n, 4, 3)
%o A120163 [A120163(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 05 2023
%Y A120163 Cf. A072493, A073941, A112088.
%K A120163 nonn
%O A120163 1,1
%A A120163 _Graeme McRae_, Jun 10 2006