A068491 - OEIS

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A068491

Expansion of Molien series for certain 4-D group of order 96.

1, 1, 2, 3, 6, 8, 13, 17, 25, 31, 42, 52, 68, 81, 101, 119, 145, 168, 200, 229, 268, 303, 349, 392, 447, 497, 560, 619, 692, 760, 843, 921, 1015, 1103, 1208, 1308, 1426, 1537, 1667, 1791, 1935, 2072, 2230, 2381, 2554, 2719, 2907, 3088, 3293, 3489, 3710, 3923, 4162 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	LINKS	`Table of n, a(n) for n=0..52.` `Index entries for Molien series`
	FORMULA	`G.f.: (x^22+x^16+x^14+x^12+x^10+x^8+x^6+1)/((1-x^2)(1-x^4)(1-x^8)*(1-x^12)).`
	EXAMPLE	`1 + x^2 + 2x^4 + 3x^6 + 6x^8 + 8x^10 + 13x^12 + 17x^14 + 25x^16 + 31x^18 + ...`
	PROG	`(MAGMA) // Definition of group: F<al> := CyclotomicField(12); w := al^4; i := al^3; s3 := (1+2*w)/i; M := GeneralLinearGroup(4, F);` `g1 := M![ 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0 ]; g2 := M![ -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]; g3 := M![ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1 ];` `H := M![ 0, -1/s3, -1/s3, -1/s3, 1/s3, 0, 1/s3, -1/s3, 1/s3, -1/s3, 0, 1/s3, 1/s3, 1/s3, -1/s3, 0 ]; G := sub<M\| g1, g2, g3, H>;`
	CROSSREFS	`Sequence in context: A101136 A036957 A022943 * A024788 A004101 A003405` `Adjacent sequences: A068488 A068489 A068490 * A068492 A068493 A068494`
	KEYWORD	`nonn`
	AUTHOR	`N. J. A. Sloane, Dec 31 2002`
	STATUS	`approved`

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Last modified May 21 05:51 EDT 2013. Contains 225474 sequences.