A120163 a(n) = 4 + floor((3 + Sum_{j=1..n-1} a(j))/4).

4, 5, 7, 8, 10, 13, 16, 20, 25, 31, 39, 49, 61, 76, 95, 119, 149, 186, 233, 291, 364, 455, 568, 710, 888, 1110, 1387, 1734, 2168, 2710, 3387, 4234, 5292, 6615, 8269, 10336, 12920, 16150, 20188, 25235

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) >;
A120163:= func< n | g(n, 4, 3) >;
[A120163(n): n in [1..60]]; // G. C. Greubel, Sep 05 2023

Mathematica

l={4};Do[l=AppendTo[l,Floor[(19+Total[l])/4]],{40}];l (* Harvey P. Dale, Sep 23 2011 *)

SageMath

@CachedFunction
def f(n, p, q): return p + (q + sum(f(k, p, q) for k in range(1, n)))//4
def A120163(n): return f(n, 4, 3)
[A120163(n) for n in range(1, 61)] # G. C. Greubel, Sep 05 2023