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A120171 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/5).

%I A120171 #13 Jun 02 2025 00:29:31
%S A120171 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 A120171 180,216,259,311,373,448,537,645,774,929,1114,1337,1605,1926,2311,
%U A120171 2773,3328,3993,4792,5750,6900,8280,9936,11923,14308,17170,20604,24724,29669
%N A120171 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/5).
%H A120171 G. C. Greubel, <a href="/A120171/b120171.txt">Table of n, a(n) for n = 1..10000</a>
%t A120171 f[s_] := Append[s, Floor[(11 + Plus @@ s)/5]]; Nest[f, {2}, 53] (* _Robert G. Wilson v_, Jul 08 2006 *)
%o A120171 (Magma)
%o A120171 function f(n, a, b)
%o A120171   t:=0;
%o A120171     for k in [1..n-1] do
%o A120171       t+:= a+Floor((b+t)/5);
%o A120171     end for;
%o A120171   return t;
%o A120171 end function;
%o A120171 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120171 A120171:= func< n | g(n, 2, 1) >;
%o A120171 [A120171(n): n in [1..60]]; // _G. C. Greubel_, Dec 25 2023
%o A120171 (SageMath)
%o A120171 @CachedFunction
%o A120171 def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
%o A120171 def A120171(n): return f(n, 2, 1)
%o A120171 [A120171(n) for n in range(1, 61)] # _G. C. Greubel_, Dec 25 2023
%Y A120171 Cf. A073941, A072493, A112088.
%K A120171 nonn
%O A120171 1,1
%A A120171 _Graeme McRae_, Jun 10 2006
%E A120171 More terms from _Robert G. Wilson v_, Jul 08 2006