A120164 a(n) = 6 + floor( Sum_{j=1..n-1} a(j)/4 ).

6, 7, 9, 11, 14, 17, 22, 27, 34, 42, 53, 66, 83, 103, 129, 161, 202, 252, 315, 394, 492, 615, 769, 961, 1202, 1502, 1878, 2347, 2934, 3667, 4584, 5730, 7163, 8953, 11192, 13990, 17487, 21859, 27324, 34155

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. A072493, A073941, A112088.

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) >;
A120164:= func< n | g(n, 6, 0) >;
[A120164(n): n in [1..60]]; // G. C. Greubel, Sep 05 2023

Mathematica

f[n_, p_, q_]:= f[n, p, q]= p +Quotient[q +Sum[f[k,p,q], {k,n-1}], 4];
A120164[n_]:= f[n,6,0];
Table[A120164[n], {n, 60}] (* G. C. Greubel, Sep 05 2023 *)

SageMath

@CachedFunction
def f(n,p,q): return p + (q +sum(f(k,p,q) for k in range(1, n)))//4
def A120164(n): return f(n, 6, 0)
[A120164(n) for n in range(1, 61)] # G. C. Greubel, Sep 05 2023