A120167 a(n) = 9 + floor((3 + Sum_{j=1..n-1} a(j))/4).

9, 12, 15, 18, 23, 29, 36, 45, 56, 70, 88, 110, 137, 171, 214, 268, 335, 418, 523, 654, 817, 1021, 1277, 1596, 1995, 2494, 3117, 3896, 4870, 6088, 7610, 9512, 11890, 14863, 18579, 23223, 29029, 36286, 45358, 56697

Offset: 1

Author

Graeme McRae, Jun 10 2006

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A072493, A073941, A112088.

Cf. A120160 - A120166, A120168, 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) >;
A120167:= func< n | g(n, 9, 3) >;
[A120167(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023

Mathematica

nxt[{t_,a_}]:=Module[{c=Floor[(39+t)/4]},{t+c,c}]; NestList[nxt,{9,9},40][[All,2]] (* Harvey P. Dale, Apr 24 2019 *)

SageMath

@CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120167(n): return f(n, 9, 3)
[A120167(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023