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A112088
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Number of leaf nodes in a binary tree.
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77
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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; internal format)
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OFFSET
| 1,1
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LINKS
| David W. Wilson, Table of n, a(n) for n=1..1000
Simon Strandgaard, About this sequence
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FORMULA
| a(1)=2; a(n)=floor((5+sum(a(1) to a(n-1)))/2) - Graeme McRae (g_m(AT)mcraefamily.com), Jun 09 2006
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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 (rgwv(at)rgwv.com), Jan 11 2006 *))
f[s_] := Append[s, Ceiling[2 + Plus @@ s/2]]; Nest[f, {2}, 38] (* Robert G. Wilson v (rgwv(at)rgwv.com), Jul 08 2006 *)
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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);
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CROSSREFS
| Sequence in context: A023435 A091501 A083198 * A117792 A154888 A018057
Adjacent sequences: A112085 A112086 A112087 * A112089 A112090 A112091
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KEYWORD
| easy,nonn
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AUTHOR
| Simon Strandgaard (neoneye(AT)gmail.com), Nov 29 2005
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EXTENSIONS
| More terms from Simon Strandgaard (neoneye(AT)gmail.com), Nov 29 2005
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