A120170 a(n) = ceiling( Sum_{i=1..n-1} a(i)/5 ), a(1)=1.

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, 89, 107, 128, 154, 185, 222, 266, 319, 383, 460, 552, 662, 795, 954, 1144, 1373, 1648, 1977, 2373, 2847, 3417, 4100, 4920, 5904, 7085, 8502, 10202, 12243, 14691, 17630

Offset: 1

Author

Graeme McRae, Jun 10 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Magma

function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Ceiling ((b+t)/5);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120170:= func< n | n eq 1 select 1 else g(n-1, 1, -4) >;
[A120170(n): n in [1..60]]; // G. C. Greubel, Dec 25 2023

Mathematica

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

SageMath

@CachedFunction
def a(n):
    if (n==1): return 1
    else: return ceil(sum(a(k)/5 for k in (1..n-1)))
[a(n) for n in (1..60)] # G. C. Greubel, Aug 19 2019

Extensions

Edited and extended by Robert G. Wilson v, Jul 07 2006