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A006327
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Fibonacci numbers - 3. Number of total preorders.
(Formerly M1371)
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18
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0, 2, 5, 10, 18, 31, 52, 86, 141, 230, 374, 607, 984, 1594, 2581, 4178, 6762, 10943, 17708, 28654, 46365, 75022, 121390, 196415, 317808, 514226, 832037, 1346266, 2178306, 3524575, 5702884, 9227462, 14930349
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| Minimal cost of maximum height Huffman tree of size n. - Alex Vinokur (alexvn(AT)barak-online.net), Oct 25 2004
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REFERENCES
| G. Kreweras, Les preordres totaux compatibles avec un ordre partiel. Math. Sci. Humaines No. 53 (1976), 5-30.
A. Sapounakis, I. Tasoulas and P. Tsikouras, On the Dominance Partial Ordering of Dyck Paths, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.5.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Alex Vinokur, Fibonacci connection between Huffman codes and Wythoff array, E-print
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FORMULA
| G.f.: x^3*(2 + x)/((1-x)*(1-x-x^2)); a(n) = a(n-1) + a(n-2) + 3.
a(n+3)=sum{k=-n+1..n, F(abs(n)+1)}; - Paul Barry (pbarry(AT)wit.ie), Oct 24 2007
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MAPLE
| with(combinat):a:=n->sum(fibonacci(j), j=3..n): seq(a(n), n=2..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007
A006327:=(2+z)/(z-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Fibonacci[Range[4, 5! ]]-3 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 19 2010]
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CROSSREFS
| A diagonal of A079502.
Cf. A000045, A001611, A000071, A157725, A001911, A157726, A006327, A157727, A157728, A157729, A167616. [Added by N. J. A. Sloane, Jun 25 2010 in response to a comment from Aviezri S. Fraenkel]
Sequence in context: A117485 A084835 A034350 * A185721 A103577 A079006
Adjacent sequences: A006324 A006325 A006326 * A006328 A006329 A006330
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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