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%I M4851 #22 Feb 12 2023 16:16:00
%S 1,12,81,372,1332,3984,10420,24540,53145,107436,205065,372792,649936,
%T 1092672,1779408,2817288,4350105,6567660,9716905,14114892,20163924,
%U 28368912,39357396,53902212,72947329,97636812,129347505,169725360,220726080,284659968,364241728
%N Number of 4-voter voting schemes with n linearly ranked choices.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Colin Barker, <a href="/A007010/b007010.txt">Table of n, a(n) for n = 1..1000</a>
%H Daniel E. Loeb, <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. [broken link]
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,2,27,-36,0,36,-27,-2,12,-6,1).
%F G.f.: x*(1+6*x+21*x^2+28*x^3+21*x^4+6*x^5+x^6)/((1+x)^3*(1-x)^9). - _Ralf Stephan_, Apr 23 2004
%F From _Colin Barker_, Jan 07 2016: (Start)
%F a(n) = (n^8+16*n^7+106*n^6+376*n^5+784*n^4+1024*n^3+864*n^2+384*n)/3840 for n even.
%F a(n) = (n^8+16*n^7+106*n^6+376*n^5+784*n^4+1024*n^3+894*n^2+504*n+135)/3840 for n odd.
%F (End)
%t LinearRecurrence[{6,-12,2,27,-36,0,36,-27,-2,12,-6,1},{1,12,81,372,1332,3984,10420,24540,53145,107436,205065,372792},40] (* _Harvey P. Dale_, Feb 12 2023 *)
%o (PARI) Vec(x*(1+6*x+21*x^2+28*x^3+21*x^4+6*x^5+x^6)/((1+x)^3*(1-x)^9) + O(x^100)) \\ _Colin Barker_, Jan 07 2016
%K nonn,easy
%O 1,2
%A _Daniel E. Loeb_
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