A007010 Number of 4-voter voting schemes with n linearly ranked choices. (Formerly M4851)

1, 12, 81, 372, 1332, 3984, 10420, 24540, 53145, 107436, 205065, 372792, 649936, 1092672, 1779408, 2817288, 4350105, 6567660, 9716905, 14114892, 20163924, 28368912, 39357396, 53902212, 72947329, 97636812, 129347505, 169725360, 220726080, 284659968, 364241728

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Daniel E. Loeb, On Games, Voting Schemes and Distributive Lattices. LaBRI Report 625-93, University of Bordeaux I, 1993. [broken link]

Index entries for linear recurrences with constant coefficients, signature (6,-12,2,27,-36,0,36,-27,-2,12,-6,1).

Formula

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

From Colin Barker, Jan 07 2016: (Start)

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.

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.

(End)

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A009500 A012195 A147650 * A069996 A183504 A194493

Adjacent sequences: A007007 A007008 A007009 * A007011 A007012 A007013

Keyword

nonn,easy

Author

Daniel E. Loeb

Status

approved