A120171 - OEIS

%I #11 Dec 26 2023 15:34:48

%S 2,2,3,3,4,5,6,7,8,10,12,14,17,20,24,29,35,42,50,60,72,87,104,125,150,

%T 180,216,259,311,373,448,537,645,774,929,1114,1337,1605,1926,2311,

%U 2773,3328,3993,4792,5750,6900,8280,9936,11923,14308,17170,20604,24724,29669

%N a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/5)

%H G. C. Greubel, <a href="/A120171/b120171.txt">Table of n, a(n) for n = 1..10000</a>

%t f[s_] := Append[s, Floor[(11 + Plus @@ s)/5]]; Nest[f, {2}, 53] (* _Robert G. Wilson v_, Jul 08 2006 *)

%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)/5);

%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 A120171:= func< n | g(n, 2, 1) >;

%o [A120171(n): n in [1..60]]; // _G. C. Greubel_, Dec 25 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)))//5

%o def A120171(n): return f(n, 2, 1)

%o [A120171(n) for n in range(1, 61)] # _G. C. Greubel_, Dec 25 2023

%Y Cf. A073941, A072493, A112088.

%K nonn

%O 1,1

%A _Graeme McRae_, Jun 10 2006

%E More terms from _Robert G. Wilson v_, Jul 08 2006