A131769 Number of connected components in the double Bruhat cells for simple Lie groups of type B_n (or C_n).

8, 30, 72, 160, 352, 768, 1664, 3584, 7680, 16384, 34816, 73728, 155648, 327680, 688128, 1441792, 3014656, 6291456, 13107200, 27262976

Offset

2,1

Comments

See A060344 for the corresponding result for Lie groups of type A_n.

Links

Table of n, a(n) for n=2..21.

Michael Gekhtman et al., The number of connected components in the double Bruhat cells for nonsimply-laced groups.

Formula

a(2) = 8, a(3) = 30 and a(n) = (n+5)*2^(n-1) for n >= 4.

G.f.: 2*x^2*(4-x-8*x^2-4*x^3)/(1-2*x)^2. a(n) = 4*(a(n-1)-a(n-2)) for n >= 6. [Colin Barker, Feb 10 2012]

Crossrefs

Cf. A060344.

Sequence in context: A184323 A004639 A317637 * A055832 A195753 A100175

Adjacent sequences: A131766 A131767 A131768 * A131770 A131771 A131772

Keyword

easy,nonn

Author

Peter Bala, Jul 14 2007

Status

approved