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A120173 a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/5).

%I A120173 #7 Dec 26 2023 11:23:16
%S A120173 4,5,6,7,9,10,12,15,18,21,26,31,37,44,53,64,77,92,110,132,159,191,229,
%T A120173 275,330,396,475,570,684,821,985,1182,1418,1702,2042,2451,2941,3529,
%U A120173 4235,5082
%N A120173 a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/5).
%H A120173 G. C. Greubel, <a href="/A120173/b120173.txt">Table of n, a(n) for n = 1..10000</a>
%t A120173 A120173[n_]:= A120173[n]= 4 +Floor[(3 +Sum[a[j], {j,n-1}])/5];
%t A120173 Table[A120173[n], {n, 60}] (* _G. C. Greubel_, Dec 26 2023 *)
%o A120173 (Magma)
%o A120173 function f(n, a, b)
%o A120173   t:=0;
%o A120173     for k in [1..n-1] do
%o A120173       t+:= a+Floor((b+t)/5);
%o A120173     end for;
%o A120173   return t;
%o A120173 end function;
%o A120173 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120173 A120173:= func< n | g(n, 4, 3) >;
%o A120173 [A120173(n): n in [1..60]]; // _G. C. Greubel_, Dec 26 2023
%o A120173 (SageMath)
%o A120173 @CachedFunction
%o A120173 def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
%o A120173 def A120173(n): return f(n, 4, 3)
%o A120173 [A120173(n) for n in range(1, 61)] # _G. C. Greubel_, Dec 26 2023
%Y A120173 Cf. A073941, A072493, A112088.
%K A120173 nonn
%O A120173 1,1
%A A120173 _Graeme McRae_, Jun 10 2006