Search: id:A065220
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%I A065220
%S A065220 0,0,1,1,1,0,2,6,13,25,45,78,132,220,363,595,971,1580,2566,4162,6745,10925,
               17689,
%T A065220 28634,46344,75000,121367,196391,317783,514200,832010,1346238,2178277,
               3524545,5702853,
%U A065220 9227430,14930316,24157780,39088131,63245947,102334115,165580100,267914254
%V A065220 0,0,-1,-1,-1,0,2,6,13,25,45,78,132,220,363,595,971,1580,2566,4162,6745,
               10925,17689,
%W A065220 28634,46344,75000,121367,196391,317783,514200,832010,1346238,2178277,
               3524545,5702853,
%X A065220 9227430,14930316,24157780,39088131,63245947,102334115,165580100,267914254
%N A065220 Fib(n)-n.
%C A065220 E(n)=Fib(n+4)-(n+4): cost of maximum height Huffman tree of size n for 
               Fibonacci sequence (Fibonacci sequence is minimizing _absolutely_ 
               ordered sequence of Huffman tree). - Alex Vinokur (alexvn(AT)barak-online.net), 
               Oct 26 2004
%D A065220 Vinokur A.B, Huffman trees and Fibonacci numbers, Kibernetika Issue 6 
               (1986) 9-12 (in Russian); English translation in Cybernetics 21, 
               Issue 6 (1986), 692-696.
%H A065220 Harry J. Smith, <a href="b065220.txt">Table of n, a(n) for n=0,...,300</
               a>
%H A065220 Alex Vinokur, <a href="http://arXiv.org/abs/cs/0410013">Fibonacci connection 
               between Huffman codes and Wythoff array</a>, E-print
%H A065220 Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003.html">
               International Contest Of Logical Sequences</a>, 2002 - 2003. Item 
               7
%H A065220 Albert Frank, <a href="http://www.paulcooijmans.com/oth/intcont2003ans.html">
               Solutions of International Contest Of Logical Sequences</a>, 2002 
               - 2003.
%F A065220 a(n) =A000045(n)-A001477(n) =a(n-1)+a(n-2)+n-3 =a(n-1)+A000071(n-2) =A000126(n-3)-2 
               =A001924(n-4)-1. G.f. x^2*(2x-1)/((1-x-x^2)*(1-x)^2)
%p A065220 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+a[n-2] od: seq(a[n]-n, 
               n=0..42); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 
               2008
%p A065220 a:=n->sum(fibonacci(i,1)-1, i=0..n): seq(a(n), n=-2..40); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
%t A065220 lst={};Do[f=Fibonacci[n]-n;AppendTo[lst,f],{n,0,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Mar 21 2009]
%o A065220 (PARI) { for (n=0, 300, write("b065220.txt", n, " ", fibonacci(n) - n) 
               ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 14 2009]
%Y A065220 Sequence in context: A011891 A003600 A000135 this_sequence A048094 A031872 
               A124677
%Y A065220 Adjacent sequences: A065217 A065218 A065219 this_sequence A065221 A065222 
               A065223
%K A065220 easy,sign
%O A065220 0,7
%A A065220 Henry Bottomley (se16(AT)btinternet.com), Oct 22 2001

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