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

3, 4, 4, 5, 6, 7, 9, 11, 13, 15, 18, 22, 26, 32, 38, 46, 55, 66, 79, 95, 114, 137, 164, 197, 236, 283, 340, 408, 490, 588, 705, 846, 1015, 1218, 1462, 1754, 2105, 2526, 3031, 3638, 4365, 5238, 6286, 7543, 9052, 10862, 13034, 15641, 18769, 22523, 27028, 32433

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) >;
A120172:= func< n | g(n, 3, 2) >;
[A120172(n): n in [1..60]]; // G. C. Greubel, Dec 25 2023

Mathematica

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 *)

SageMath

@CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//5
def A120172(n): return f(n, 3, 2)
[A120172(n) for n in range(1, 61)] # G. C. Greubel, Dec 25 2023

Extensions

More terms from Harvey P. Dale, Jun 11 2014