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A023548
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Convolution of natural numbers >= 2 and Fibonacci numbers.
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10
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2, 5, 11, 21, 38, 66, 112, 187, 309, 507, 828, 1348, 2190, 3553, 5759, 9329, 15106, 24454, 39580, 64055, 103657, 167735, 271416, 439176, 710618, 1149821, 1860467, 3010317, 4870814, 7881162
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Minimal cost of maximum height Huffman tree of size n for strictly "worst case height" sequences. (A strictly "worst case height" sequence generates only maximum height Huffman trees; a non-strictly "worst case height" sequence can generate also non-maximum height Huffman trees.) - Alex Vinokur (alexvn(AT)barak-online.net), Oct 26 2004
Record-positions for A107910: A107910(a(n+2))=A005578(n), A107910(m) < A005578(n) for m<a(n+2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 28 2005
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REFERENCES
| 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
| Alex Vinokur, Fibonacci connection between Huffman codes and Wythoff array, E-print
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FORMULA
| a(n)=4*(F(n+1)-1)+3*F(n)-n; F(n)=A000045 (Fibonacci): G.F. x*(2-x)/((1-x-x^2)*(1-x)^2). Also convolution of natural numbers n >= 1 with Lucas numbers (A000032) - from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
For n>=1, a(n)=L(n+3)-(n+4), where L(n) are Lucas numbers. - Mario Catalani (mario.catalani(AT)unito.it), Jul 22 2004
Fib(n+3)+F(n+1)-(n+3) for n > 1. - Alex Vinokur (alexvn(AT)barak-online.net), Oct 26 2004
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MATHEMATICA
| a=0; b=0; c=0; lst={}; Do[z=a+b+c+1; AppendTo[lst, z]; a=b; b=c; c=z, {a, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 17 2010]
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CROSSREFS
| Cf. A006327.
Sequence in context: A112805 A119970 A082775 * A144700 A000785 A049936
Adjacent sequences: A023545 A023546 A023547 * A023549 A023550 A023551
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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