A120163 - OEIS

%I #10 Sep 06 2023 01:39:19

%S 4,5,7,8,10,13,16,20,25,31,39,49,61,76,95,119,149,186,233,291,364,455,

%T 568,710,888,1110,1387,1734,2168,2710,3387,4234,5292,6615,8269,10336,

%U 12920,16150,20188,25235

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

%H G. C. Greubel, <a href="/A120163/b120163.txt">Table of n, a(n) for n = 1..1000</a>

%t l={4};Do[l=AppendTo[l,Floor[(19+Total[l])/4]],{40}];l (* _Harvey P. Dale_, Sep 23 2011 *)

%o (Magma)

%o function f(n, a, b)

%o   t:=0;

%o     for k in [1..n-1] do

%o       t+:= a+Floor((b+t)/4);

%o     end for;

%o   return t;

%o end function;

%o g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;

%o A120163:= func< n | g(n, 4, 3) >;

%o [A120163(n): n in [1..60]]; // _G. C. Greubel_, Sep 05 2023

%o (SageMath)

%o @CachedFunction

%o def f(n, p, q): return p + (q + sum(f(k, p, q) for k in range(1, n)))//4

%o def A120163(n): return f(n, 4, 3)

%o [A120163(n) for n in range(1, 61)] # _G. C. Greubel_, Sep 05 2023

%Y Cf. A072493, A073941, A112088.

%K nonn

%O 1,1

%A _Graeme McRae_, Jun 10 2006