A120134 a(n) = 4 + floor(Sum_{k=1..n-1} a(k) / 2).

4, 6, 9, 13, 20, 30, 45, 67, 101, 151, 227, 340, 510, 765, 1148, 1722, 2583, 3874, 5811, 8717, 13075, 19613, 29419, 44129, 66193, 99290, 148935, 223402, 335103, 502655, 753982, 1130973, 1696460, 2544690, 3817035, 5725552, 8588328, 12882492

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. A073941, A072493, A112088, A120135 - A120209, A172161.

Programs

Maple

a := proc(n) option remember; 4 + iquo(add(a(k), k = 1..n-1), 2) end:
seq(a(n), n = 1..37); # Peter Luschny, May 07 2023

Mathematica

f[s_]:= Append[s, 4+Floor[Plus @@ s/2]]; Nest[f, {4}, 37] (* Robert G. Wilson v, Jun 10 2006 *)

SageMath

@CachedFunction
def A120134(n): return 4 + sum(A120134(k) for k in range(1,n))//2
print([A120134(n) for n in range(1,41)])  # G. C. Greubel, May 07 2023

Formula

a(n) ~ c * (3/2)^n, where c = 3.9320886310283094862025842648411406926537121258867950257873967568454133192... - Vaclav Kotesovec, May 07 2023

Extensions

Name edited by Peter Luschny, May 07 2023