login
A112088
Number of leaf nodes in a binary tree.
79
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
KEYWORD
easy,nonn
AUTHOR
Simon Strandgaard, Nov 29 2005
STATUS
approved