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a(n) = 2^(floor((n-1)/2)) - n*(n-1)/2.
2

%I #12 Dec 22 2016 12:01:24

%S 1,0,-1,-4,-6,-11,-13,-20,-20,-29,-23,-34,-14,-27,23,8,120,103,341,

%T 322,814,793,1795,1772,3796,3771,7841,7814,15978,15949,32303,32272,

%U 65008,64975,130477,130442,261478,261441,523547,523508,1047756,1047715

%N a(n) = 2^(floor((n-1)/2)) - n*(n-1)/2.

%C Lower bound for the essential dimension of algebraic groups with a nontrivial center.

%C 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.

%H G. C. Greubel, <a href="/A163417/b163417.txt">Table of n, a(n) for n = 1..1000</a>

%H Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli, <a href="http://arXiv.org/abs/math/0701903">Essential Dimension and Algebraic Stacks</a>, arXiv:math/0701903 [math.AG], 2007.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,6,-2).

%F From _R. J. Mathar_, Sep 27 2009: (Start)

%F a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +6*a(n-4) -2*a(n-5).

%F G.f.: x*(-1-4*x^3+x^4+3*x)/((2*x^2-1)*(1-x)^3). (End)

%t LinearRecurrence[{3,-1,-5,6,-2}, {1, 0, -1, -4, -6}, 50] (* _G. C. Greubel_, Dec 21 2016 *)

%o (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

%K easy,sign

%O 1,4

%A _Jonathan Vos Post_, Jul 27 2009

%E Edited (but not checked) by _N. J. A. Sloane_, Aug 01 2009