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

1,1

Links

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

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 *)

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

Crossrefs

Cf. A072493, A073941, A112088.

Cf. A120160 - A120166, A120168, A120169.

Sequence in context: A161345 A102655 A308748 * A263674 A337701 A048699

Adjacent sequences: A120164 A120165 A120166 * A120168 A120169 A120170

Keyword

nonn,easy

Author

Graeme McRae, Jun 10 2006

Status

approved