A120166 a(n) = 8 + floor((2 + Sum_{j=1..n-1} a(j))/4).

8, 10, 13, 16, 20, 25, 31, 39, 49, 61, 76, 95, 119, 149, 186, 232, 290, 363, 454, 567, 709, 886, 1108, 1385, 1731, 2164, 2705, 3381, 4226, 5283, 6603, 8254, 10318, 12897, 16121, 20152, 25190, 31487, 39359, 49199

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 - A120165, 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) >;
A120166:= func< n | g(n, 8, 2) >;
[A120166(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];
A120166[n_]:= f[n,8,2];
Table[A120166[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 A120166(n): return f(n, 8, 2)
[A120166(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023