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

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, 180, 216, 259, 311, 373, 448, 537, 645, 774, 929, 1114, 1337, 1605, 1926, 2311, 2773, 3328, 3993, 4792, 5750, 6900, 8280, 9936, 11923, 14308, 17170, 20604, 24724, 29669

Offset: 1

Author

Graeme McRae, Jun 10 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073941, A072493, A112088.

Programs

Magma

function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/5);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120171:= func< n | g(n, 2, 1) >;
[A120171(n): n in [1..60]]; // G. C. Greubel, Dec 25 2023

Mathematica

f[s_] := Append[s, Floor[(11 + Plus @@ s)/5]]; Nest[f, {2}, 53] (* Robert G. Wilson v, Jul 08 2006 *)

SageMath

@CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
def A120171(n): return f(n, 2, 1)
[A120171(n) for n in range(1, 61)] # G. C. Greubel, Dec 25 2023

Extensions

More terms from Robert G. Wilson v, Jul 08 2006