OFFSET
1,4
COMMENTS
Lower bound for the essential dimension of algebraic groups with a nontrivial center.
See Theorem 1.13, p.4. The essential dimension ed a of a (with respect to L) is the minimum of the transcendence degrees tr deg_k K taken over all fields of definition of a. Suppose k is a field of characteristic not equal to 2, and that sqrt(-1) is an element of k. If n is not divisible by 4 then a(n) <= ed Spin_n <= 2^(floor((n-1)/2)). If n is divisible by 4 then a(n) + 1 <= ed Spin_n <= 2^(floor((n-1)/2)) + 1.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli, Essential Dimension and Algebraic Stacks, arXiv:math/0701903 [math.AG], 2007.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,6,-2).
FORMULA
From R. J. Mathar, Sep 27 2009: (Start)
a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +6*a(n-4) -2*a(n-5).
G.f.: x*(-1-4*x^3+x^4+3*x)/((2*x^2-1)*(1-x)^3). (End)
MATHEMATICA
LinearRecurrence[{3, -1, -5, 6, -2}, {1, 0, -1, -4, -6}, 50] (* G. C. Greubel, Dec 21 2016 *)
PROG
(PARI) Vec(x*(-1-4*x^3+x^4+3*x)/((2*x^2-1)*(1-x)^3) + O(x^50)) \\ G. C. Greubel, Dec 21 2016
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Jonathan Vos Post, Jul 27 2009
EXTENSIONS
Edited (but not checked) by N. J. A. Sloane, Aug 01 2009
STATUS
approved