A112088 Number of leaf nodes in a binary tree.

2, 3, 5, 7, 11, 16, 24, 36, 54, 81, 122, 183, 274, 411, 617, 925, 1388, 2082, 3123, 4684, 7026, 10539, 15809, 23713, 35570, 53355, 80032, 120048, 180072, 270108, 405162, 607743, 911615, 1367422, 2051133, 3076700, 4615050, 6922575, 10383862

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5678 (terms 1..1000 from David W. Wilson)

Simon Strandgaard, About this sequence

Formula

a(1)=2; a(n) = floor((5 + Sum_{j=1..n-1} a(j))/2). - Graeme McRae, Jun 09 2006

a(n) ~ c * 3^n / 2^n, where c = 1.4086393347913639409553312264320529315790457870253974319560288484955... - Vaclav Kotesovec, Dec 26 2023

Maple

a:=2; b:=0; c:=4; p := proc() local x; global a, b, c; x := b + a; c := c - x; if(c<0) then a := a*2; c := c + a*2; end if; b := floor((a*2-c+1) / 2); x end proc: seq(p(), i=0..40);

Mathematica

f[n_] := Block[{a = 2, b = 0, c = 4}, Do[x = b + a; c -= x; If[c < 0, a *= 2; c += 2a]; b = Floor[(2a - c + 1)/2], {i, n}]; x]; Array[f, 40] (* Robert G. Wilson v, Jan 11 2006 *))
f[s_] := Append[s, Ceiling[2 + Plus @@ s/2]]; Nest[f, {2}, 38] (* Robert G. Wilson v, Jul 08 2006 *)

Prog

(Ruby) a, c=2, 4; p Array.new(99){c-=x=(a*4-c+1)/2; c+=2*a*=2 if c<0; x}
(PARI) first(n)=my(v=vector(n), s); v[1]=s=2; for(n=2, n, s+=v[n]=(s+5)\2); v \\ Charles R Greathouse IV, Nov 07 2016

Crossrefs

Sequence in context: A286271 A083198 A333589 * A333588 A117792 A154888

Adjacent sequences: A112085 A112086 A112087 * A112089 A112090 A112091

Keyword

easy,nonn

Author

Simon Strandgaard, Nov 29 2005

Status

approved