A120170 - OEIS

%I #16 Dec 27 2023 08:09:32

%S 1,1,1,1,1,1,2,2,2,3,3,4,5,6,7,8,10,12,14,17,21,25,30,36,43,52,62,74,

%T 89,107,128,154,185,222,266,319,383,460,552,662,795,954,1144,1373,

%U 1648,1977,2373,2847,3417,4100,4920,5904,7085,8502,10202,12243,14691,17630

%N a(n) = ceiling( Sum_{i=1..n-1} a(i)/5 ), a(1)=1.

%H G. C. Greubel, <a href="/A120170/b120170.txt">Table of n, a(n) for n = 1..1000</a>

%t f[s_] := Append[s, Ceiling[Plus @@ s/5]]; Nest[f, {1}, 57] (* _Robert G. Wilson v_, Jul 07 2006 *)

%o (SageMath)

%o @CachedFunction

%o def a(n):

%o     if (n==1): return 1

%o     else: return ceil(sum(a(k)/5 for k in (1..n-1)))

%o [a(n) for n in (1..60)] # _G. C. Greubel_, Aug 19 2019

%o (Magma)

%o function f(n, a, b)

%o   t:=0;

%o     for k in [1..n-1] do

%o       t+:= a+Ceiling ((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 A120170:= func< n | n eq 1 select 1 else g(n-1, 1, -4) >;

%o [A120170(n): n in [1..60]]; // _G. C. Greubel_, Dec 25 2023

%Y Cf. A011782, A073941, A072493, A112088, A120160, A120178, A120186, A120194, A120202.

%K nonn

%O 1,7

%A _Graeme McRae_, Jun 10 2006

%E Edited and extended by _Robert G. Wilson v_, Jul 07 2006