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A007009
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Number of 3-voter voting schemes with n linearly ranked choices.
(Formerly M3435)
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1
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1, 4, 12, 27, 54, 96, 160, 250, 375, 540, 756, 1029, 1372, 1792, 2304, 2916, 3645, 4500, 5500, 6655, 7986, 9504, 11232, 13182, 15379, 17836, 20580, 23625, 27000, 30720, 34816, 39304, 44217, 49572, 55404, 61731, 68590, 76000, 84000, 92610
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| D. E. Loeb (daniel.loeb(AT)verizon.net), On Games, Voting Schemes and Distributive Lattices. LaBRI Report 625-93, University of Bordeaux I, 1993.
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FORMULA
| G.f.: (1 - x^3 ) / (1 - x)^4 (1 - x^2 )^2.
a(n) = (1/2)*Sum_{k=1..n+1} k*floor(k/2)*ceil(k/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 29 2006
G.f.: x (1 - x^3 ) / ((1 - x)^4 (1 - x^2 )^2). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 13 2008]
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MAPLE
| a := n-> (Matrix([[0$4, 1, 4, 12, 27]]). Matrix(8, (i, j)-> if (i=j-1) then 1 elif j=1 then [4, -4, -4, 10, -4, -4, 4, -1][i] else 0 fi)^n)[1, 1]; seq (a(n), n=1..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 13 2008]
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CROSSREFS
| A006009/4.
Sequence in context: A047732 A104385 A062479 * A188814 A104384 A013697
Adjacent sequences: A007006 A007007 A007008 * A007010 A007011 A007012
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KEYWORD
| nonn
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AUTHOR
| Daniel LOEB, daniel.loeb(AT)verizon.net
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 08 2000
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