Search: id:A007009
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%I A007009 M3435
%S A007009 1,4,12,27,54,96,160,250,375,540,756,1029,1372,1792,2304,2916,3645,
%T A007009 4500,5500,6655,7986,9504,11232,13182,15379,17836,20580,23625,27000,
%U A007009 30720,34816,39304,44217,49572,55404,61731,68590,76000,84000,92610
%N A007009 Number of 3-voter voting schemes with n linearly ranked choices.
%D A007009 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007009 D. E. Loeb (daniel.loeb(AT)verizon.net), <a href="http://www.labri.u-bordeaux.fr/
               ~loeb/vote.html">On Games, Voting Schemes and Distributive Lattices</
               a>. LaBRI Report 625-93, University of Bordeaux I, 1993.
%F A007009 G.f.: (1 - x^3 ) / (1 - x)^4 (1 - x^2 )^2.
%F A007009 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
%F A007009 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]
%p A007009 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]
%Y A007009 A006009/4.
%Y A007009 Sequence in context: A047732 A104385 A062479 this_sequence A104384 A013697 
               A064444
%Y A007009 Adjacent sequences: A007006 A007007 A007008 this_sequence A007010 A007011 
               A007012
%K A007009 nonn
%O A007009 1,2
%A A007009 Daniel LOEB, daniel.loeb(AT)verizon.net
%E A007009 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 08 2000

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