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

1, 3, 4, 9, 23, 61, 166, 459, 1284, 3623, 10292, 29395, 84327, 242807, 701314, 2031085, 5895951, 17150013, 49975428, 145862571, 426337773, 1247741271, 3655973226, 10723668081, 31485145902, 92524150845, 272120203908, 800931753629, 2359038637409, 6952768502473

Offset

1,2

Comments

See A005773 for the number of minimax elements in the affine Weyl group of the Lie algebra so(2n+1).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

D. I. Panyushev, Ideals of Heisenberg type and minimax elements of affine Weyl groups, arXiv:math/0311347 [math.RT], Lie Groups and Invariant Theory, Amer. Math. Soc. Translations, Series 2, Volume 213, (2005), ed. E. Vinberg

Formula

a(n) = A005773(n-1) + 2*A005773(n-2).

O.g.f.: x/2*(1+2*x)*( 1 + sqrt(1-2*x-3*x^2)/(1-3*x) ).

a(n) ~ 5*3^(n-5/2) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 25 2014

(-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

(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

Maple

A245455 := proc(n)
    coeftayl(x/2*(1+2*x)*(1+sqrt(1-2*x-3*x^2)/(1-3*x)), x=0, n);
end proc:
seq(A245455(n), n=1..30); # Wesley Ivan Hurt, Jul 26 2014

Mathematica

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 *)

Crossrefs

Cf. A005773.

Sequence in context: A049976 A032789 A299123 * A296265 A034921 A038222

Adjacent sequences: A245452 A245453 A245454 * A245456 A245457 A245458

Keyword

nonn,easy

Author

Peter Bala, Jul 22 2014

Status

approved