cp's OEIS Frontend

A245455 Number of minimax elements in the affine Weyl group of the Lie algebra so(2n).

%I A245455 #20 Sep 06 2016 14:37:52
%S A245455 1,3,4,9,23,61,166,459,1284,3623,10292,29395,84327,242807,701314,
%T A245455 2031085,5895951,17150013,49975428,145862571,426337773,1247741271,
%U A245455 3655973226,10723668081,31485145902,92524150845,272120203908,800931753629,2359038637409,6952768502473
%N A245455 Number of minimax elements in the affine Weyl group of the Lie algebra so(2n).
%C A245455 See A005773 for the number of minimax elements in the affine Weyl group of the Lie algebra so(2n+1).
%H A245455 Vincenzo Librandi, <a href="/A245455/b245455.txt">Table of n, a(n) for n = 1..1000</a>
%H A245455 D. I. Panyushev, <a href="http://arxiv.org/abs/math/0311347">Ideals of Heisenberg type and minimax elements of affine Weyl groups</a>, arXiv:math/0311347 [math.RT], Lie Groups and Invariant Theory, Amer. Math. Soc. Translations, Series 2, Volume 213, (2005), ed. E. Vinberg
%F A245455 a(n) = A005773(n-1) + 2*A005773(n-2).
%F A245455 O.g.f.: x/2*(1+2*x)*( 1 + sqrt(1-2*x-3*x^2)/(1-3*x) ).
%F A245455 a(n) ~ 5*3^(n-5/2) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jul 25 2014
%F A245455 (-n+1)*a(n) +4*(1)*a(n-1) +7*(n-3)*a(n-2) +6*(n-5)*a(n-3)=0. - _R. J. Mathar_, Sep 06 2016
%F A245455 (5*n-4)*(n-1)*a(n) +2*(-5*n^2+9*n-10)*a(n-1) -3*(5*n+1)*(n-4)*a(n-2)=0. - _R. J. Mathar_, Sep 06 2016
%p A245455 A245455 := proc(n)
%p A245455     coeftayl(x/2*(1+2*x)*(1+sqrt(1-2*x-3*x^2)/(1-3*x)), x=0, n);
%p A245455 end proc:
%p A245455 seq(A245455(n), n=1..30); # _Wesley Ivan Hurt_, Jul 26 2014
%t A245455 Rest[CoefficientList[Series[x/2*(1+2*x)*(1+Sqrt[1-2*x-3*x^2]/(1-3*x)), {x, 0, 20}], x]] (* _Vaclav Kotesovec_, Jul 25 2014 *)
%Y A245455 Cf. A005773.
%K A245455 nonn,easy
%O A245455 1,2
%A A245455 _Peter Bala_, Jul 22 2014