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A078411 Expansion of Molien series for a certain 4-D group of order 48. 2
1, 1, 3, 5, 10, 14, 23, 31, 46, 59, 80, 100, 130, 157, 196, 233, 283, 330, 392, 451, 527, 599, 689, 776, 883, 985, 1109, 1229, 1372, 1510, 1673, 1831, 2016, 2195, 2402, 2604, 2836, 3061, 3318, 3569, 3853, 4130, 4442, 4747, 5089, 5423, 5795, 6160, 6565, 6961, 7399 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The first formula intersperses the terms with zeros, the second formula does not. - Colin Barker, Apr 02 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 (1,1,0,0,-2,0,0,1,1,-1).

FORMULA

G.f.: (x^16+x^12+x^10+2*x^8+x^6+x^4+1)/((1-x^2)*(1-x^4)*(1-x^6)*(1-x^8)).

G.f.: (x^8+x^6+x^5+2*x^4+x^3+x^2+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)). - Colin Barker, Apr 02 2015

EXAMPLE

1 + x^2 + 3*x^4 + 5*x^6 + 10*x^8 + 14*x^10 + 23*x^12 + 31*x^14 + 46*x^16 + ...

PROG

(MAGMA) // Definition of group: F<al> := CyclotomicField(24); M := GeneralLinearGroup(4, F);

B1 := M![ -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1 ]; C1 := M![1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0 ];

C2 := M![0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0 ]; G := sub<M | B1, C1, C2 >;

(PARI) Vec((x^8+x^6+x^5+2*x^4+x^3+x^2+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 02 2015

CROSSREFS

Subgroup of the group in A078404.

Sequence in context: A176222 A008610 A281688 * A137630 A320886 A220489

Adjacent sequences:  A078408 A078409 A078410 * A078412 A078413 A078414

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 27 2002

STATUS

approved

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Last modified November 20 02:57 EST 2018. Contains 317371 sequences. (Running on oeis4.)