id:A071930 - OEIS Search Results

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A071930

Number of words of length 2n in the two letters s and t that reduce to the identity 1 by using the relations ssTT=1, ststSS=1, and ststTT=1, where S and T are the inverses of s and t, respectively (i.e. sS=1 and tT=1). The generators s and t and the three stated relations generate the quaternion group Q4.

+0
1

0, 6, 12, 72, 240, 1056, 4032, 16512, 65280, 262656, 1047552, 4196352, 16773120, 67117056, 268419072, 1073774592, 4294901760, 17180000256, 68719214592, 274878431232, 1099510579200, 4398048608256, 17592181850112 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`a(n)=A003683(n+1)/6. No words of odd length (see the description above) reduce to 1.`
	FORMULA	`a(n)=2^(2n-2) - (-2)^(n-1)`
	CROSSREFS	`Cf. A003683.` `Adjacent sequences: A071927 A071928 A071929 this_sequence A071931 A071932 A071933` `Sequence in context: A045780 A088726 A107904 this_sequence A061520 A054883 A005402`
	KEYWORD	`nonn`
	AUTHOR	`John W. Layman and Jamaine Paddyfoot (layman(AT)math.vt.edu/jay_paddyfoot(AT)hotmail.com), Jun 14 2002`

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Last modified October 10 20:39 EDT 2008. Contains 144831 sequences.

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