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A006327
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a(n) = Fibonacci(n) - 3. Number of total preorders.
(Formerly M1371)
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20
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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, 24157814, 39088166, 63245983, 102334152, 165580138
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OFFSET
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4,2
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COMMENTS
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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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: x^5*(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, Oct 24 2007
a(n) = F(4*n) mod F(n+1) = F(n) - (F(n+4)^2 - F(n)^2)/F(2*n+4). - Gary Detlefs, Apr 02 2012
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EXAMPLE
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G.f. = 2*x^5 + 5*x^6 + 10*x^7 + 18*x^8 + 31*x^9 + 52*x^10 + 86*x^11 + ...
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MAPLE
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with(combinat):a:=n->sum(fibonacci(j), j=3..n): seq(a(n), n=2..40); # Zerinvary Lajos, Oct 03 2007
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MATHEMATICA
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PROG
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(Magma) [Fibonacci(n)-3: n in [4..45]]; // G. C. Greubel, Jul 13 2019
(Sage) [fibonacci(n)-3 for n in (4..45)] # G. C. Greubel, Jul 13 2019
(GAP) List([4..45], n-> Fibonacci(n)-3) # G. C. Greubel, Jul 13 2019
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CROSSREFS
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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]
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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