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Search: id:A065220
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| 0, 0, -1, -1, -1, 0, 2, 6, 13, 25, 45, 78, 132, 220, 363, 595, 971, 1580, 2566, 4162, 6745, 10925, 17689, 28634, 46344, 75000, 121367, 196391, 317783, 514200, 832010, 1346238, 2178277, 3524545, 5702853, 9227430, 14930316, 24157780, 39088131, 63245947, 102334115, 165580100, 267914254
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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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
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REFERENCES
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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.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,300
Alex Vinokur, Fibonacci connection between Huffman codes and Wythoff array, E-print
Albert Frank, International Contest Of Logical Sequences, 2002 - 2003. Item 7
Albert Frank, Solutions of International Contest Of Logical Sequences, 2002 - 2003.
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FORMULA
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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)
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MAPLE
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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
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
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MATHEMATICA
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lst={}; Do[f=Fibonacci[n]-n; AppendTo[lst, f], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 21 2009]
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PROGRAM
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(PARI) { for (n=0, 300, write("b065220.txt", n, " ", fibonacci(n) - n) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 14 2009]
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CROSSREFS
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Sequence in context: A011891 A003600 A000135 this_sequence A048094 A031872 A124677
Adjacent sequences: A065217 A065218 A065219 this_sequence A065221 A065222 A065223
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KEYWORD
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easy,sign
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Oct 22 2001
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