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A112088 Number of leaf nodes in a binary tree. 77
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 (list; graph; refs; listen; history; text; internal format)
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(a(1) to a(n-1)))/2). - Graeme McRae, Jun 09 2006

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}

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);

(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: A091501 A286271 A083198 * A117792 A154888 A271485

Adjacent sequences:  A112085 A112086 A112087 * A112089 A112090 A112091

KEYWORD

easy,nonn

AUTHOR

Simon Strandgaard (neoneye(AT)gmail.com), Nov 29 2005

STATUS

approved

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Last modified December 12 01:08 EST 2017. Contains 295936 sequences.