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A068491 Expansion of Molien series for a certain 4-D group of order 96. 1
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

COMMENTS

The first formula intersperses the terms with zeros, the second formula doesn't. - Colin Barker, Apr 01 2015

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,2,-2,1,0,-1,2,-1).

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)).

G.f.: (x^10-x^9+x^8+x^6+x^4+x^2-x+1) / ((x-1)^4*(x+1)^2*(x^2-x+1)*(x^2+1)*(x^2+x+1)). - Colin Barker, Apr 01 2015

EXAMPLE

1 + x^2 + 2*x^4 + 3*x^6 + 6*x^8 + 8*x^10 + 13*x^12 + 17*x^14 + 25*x^16 + 31*x^18 + ...

MATHEMATICA

LinearRecurrence[{2, -1, 0, 1, -2, 2, -2, 1, 0, -1, 2, -1}, {1, 1, 2, 3, 6, 8, 13, 17, 25, 31, 42, 52}, 60] (* Harvey P. Dale, Aug 29 2016 *)

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>;

(PARI) Vec((x^10-x^9+x^8+x^6+x^4+x^2-x+1) / ((x-1)^4*(x+1)^2*(x^2-x+1)*(x^2+1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 01 2015

CROSSREFS

Sequence in context: A036957 A251260 A022943 * A239952 A240076 A266771

Adjacent sequences:  A068488 A068489 A068490 * A068492 A068493 A068494

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 31 2002

STATUS

approved

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Last modified December 7 13:07 EST 2016. Contains 278875 sequences.