A120169 a(n) = 12 + floor((1 + Sum_{j=1..n-1} a(j))/4).

12, 15, 19, 23, 29, 36, 45, 57, 71, 89, 111, 139, 173, 217, 271, 339, 423, 529, 661, 827, 1033, 1292, 1615, 2018, 2523, 3154, 3942, 4928, 6160, 7700, 9625, 12031, 15039, 18798, 23498, 29372, 36715, 45894, 57368, 71710

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. A120149, A120160 - A120168, A120171.

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) >;
A120169:= func< n | g(n, 12, 1) >;
[A120169(n): n in [1..60]]; // G. C. Greubel, Sep 09 2023

Mathematica

nxt[{t_,a_}]:=Module[{c=Floor[(t+49)/4]},{t+c,c}]; NestList[nxt,{12,12},40][[All,2]] (* Harvey P. Dale, Jun 21 2017 *)

SageMath

@CachedFunction
def f(n, p, q): return p + (q +sum(f(k, p, q) for k in range(1, n)))//4
def A120169(n): return f(n, 12, 1)
[A120169(n) for n in range(1, 61)] # G. C. Greubel, Sep 09 2023