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

1,1

Links

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A072493, A073941, A112088.

Sequence in context: A096791 A199122 A086740 * A100665 A114095 A301513

Adjacent sequences: A120158 A120159 A120160 * A120162 A120163 A120164

Keyword

nonn

Author

Graeme McRae, Jun 10 2006

Extensions

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

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

Status

approved