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A120172 a(n) = 3 + floor((2 + Sum_{j=1..n-1} a(j))/5).

%I A120172 #11 Dec 26 2023 11:23:24
%S A120172 3,4,4,5,6,7,9,11,13,15,18,22,26,32,38,46,55,66,79,95,114,137,164,197,
%T A120172 236,283,340,408,490,588,705,846,1015,1218,1462,1754,2105,2526,3031,
%U A120172 3638,4365,5238,6286,7543,9052,10862,13034,15641,18769,22523,27028,32433
%N A120172 a(n) = 3 + floor((2 + Sum_{j=1..n-1} a(j))/5).
%H A120172 G. C. Greubel, <a href="/A120172/b120172.txt">Table of n, a(n) for n = 1..10000</a>
%t A120172 nxt[{a_,ls_}]:=Module[{x=Floor[(17+ls)/5]},{x,ls+x}]; Transpose[ NestList[ nxt,{3,3},60]][[1]] (* _Harvey P. Dale_, Jun 11 2014 *)
%o A120172 (Magma)
%o A120172 function f(n, a, b)
%o A120172   t:=0;
%o A120172     for k in [1..n-1] do
%o A120172       t+:= a+Floor((b+t)/5);
%o A120172     end for;
%o A120172   return t;
%o A120172 end function;
%o A120172 g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
%o A120172 A120172:= func< n | g(n, 3, 2) >;
%o A120172 [A120172(n): n in [1..60]]; // _G. C. Greubel_, Dec 25 2023
%o A120172 (SageMath)
%o A120172 @CachedFunction
%o A120172 def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
%o A120172 def A120172(n): return f(n, 3, 2)
%o A120172 [A120172(n) for n in range(1, 61)] # _G. C. Greubel_, Dec 25 2023
%Y A120172 Cf. A073941, A072493, A112088.
%K A120172 nonn
%O A120172 1,1
%A A120172 _Graeme McRae_, Jun 10 2006
%E A120172 More terms from _Harvey P. Dale_, Jun 11 2014