A131769 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	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.: 2x^2(4-x-8x^2-4x^3)/(1-2x)^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`

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Last modified January 27 09:05 EST 2023. Contains 359838 sequences. (Running on oeis4.)