A120162 - OEIS

%I #9 Sep 03 2023 08:41:06

%S 3,4,5,6,8,10,12,15,19,24,30,37,46,58,72,90,113,141,176,220,275,344,

%T 430,538,672,840,1050,1313,1641,2051,2564,3205,4006,5008,6260,7825,

%U 9781,12226,15283,19103

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

%H G. C. Greubel, <a href="/A120162/b120162.txt">Table of n, a(n) for n = 1..1000</a>

%t f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q + Sum[f[k,p,q], {k,n-1}], 4];

%t A120162[n_]:= f[n,3,2];

%t Table[A120162[n], {n,60}] (* _G. C. Greubel_, Sep 02 2023 *)

%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 A120162:= func< n | g(n, 3, 2) >;

%o [A120162(n): n in [1..60]]; // _G. C. Greubel_, Sep 02 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 A120162(n): return f(n,3,2)

%o [A120162(n) for n in range(1,61)] # _G. C. Greubel_, Sep 02 2023

%Y Cf. A072493, A073941, A112088.

%K nonn

%O 1,1

%A _Graeme McRae_, Jun 10 2006

%E Name edited by _G. C. Greubel_, Sep 02 2023