A120161 a(n) = 2 + floor((1 + Sum_{j=1..n-1} a(j))/4).

2, 2, 3, 4, 5, 6, 7, 9, 11, 14, 18, 22, 28, 35, 43, 54, 68, 85, 106, 132, 165, 207, 258, 323, 404, 505, 631, 789, 986, 1232, 1540, 1925, 2407, 3008, 3760, 4700, 5875, 7344, 9180, 11475, 14344, 17930, 22412, 28015, 35019, 43774, 54717, 68397, 85496, 106870

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) >;
A120161:= func< n | g(n,2,1) >;
[A120161(n): n in [1..60]]; // G. C. Greubel, Sep 02 2023

Mathematica

f[s_]:= Append[s, Floor[(9 +Plus @@ s)/4]]; Nest[f, {2}, 49] (* Robert G. Wilson v, Jul 08 2006 *)

SageMath

@CachedFunction
def f(n,p,q): return p + (q + sum(f(k,p,q) for k in range(1,n)))//4
def A120161(n): return f(n,2,1)
[A120161(n) for n in range(1,61)] # G. C. Greubel, Sep 02 2023

Extensions

More terms from Robert G. Wilson v, Jul 08 2006

Name edited by G. C. Greubel, Sep 02 2023