A120168 a(n) = 11 + floor(Sum_{j-1..n-1} a(j)/4).

11, 13, 17, 21, 26, 33, 41, 51, 64, 80, 100, 125, 156, 195, 244, 305, 381, 476, 595, 744, 930, 1163, 1453, 1817, 2271, 2839, 3548, 4435, 5544, 6930, 8663, 10828, 13535, 16919, 21149, 26436, 33045, 41306, 51633, 64541

Offset: 1

Author

Graeme McRae, Jun 10 2006

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A072493, A073941, A112088.

Cf. A120160 - A120167, A120169.

Programs

Magma

function f(n, a, b)
  t:=0;
    for k in [1..n-1] do
      t+:= a+Floor((b+t)/4);
    end for;
  return t;
end function;
g:= func< n, a, b | f(n+1, a, b)-f(n, a, b) >;
A120168:= func< n | g(n, 11, 0) >;
[A120168(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023

Mathematica

f[n_, p_, q_]:= f[n,p,q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
A120168[n_]:= f[n, 11, 0];
Table[A120168[n], {n, 60}] (* G. C. Greubel, Sep 09 2023 *)

SageMath

@CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120168(n): return f(n, 11, 0)
[A120168(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023