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A245455 Number of minimax elements in the affine Weyl group of the Lie algebra so(2n). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A032789 A089243 A299123 * A296265 A034921 A038222

Adjacent sequences:  A245452 A245453 A245454 * A245456 A245457 A245458

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Jul 22 2014

STATUS

approved

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Last modified February 23 11:41 EST 2018. Contains 299579 sequences. (Running on oeis4.)