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A008612 Molien series of 2-dimensional representation of SL(2,3). 1
1, 0, 0, 1, 1, 0, 2, 1, 1, 2, 2, 1, 3, 2, 2, 3, 3, 2, 4, 3, 3, 4, 4, 3, 5, 4, 4, 5, 5, 4, 6, 5, 5, 6, 6, 5, 7, 6, 6, 7, 7, 6, 8, 7, 7, 8, 8, 7, 9, 8, 8, 9, 9, 8, 10, 9, 9, 10, 10, 9, 11, 10, 10, 11, 11, 10, 12, 11, 11, 12, 12, 11, 13, 12, 12, 13, 13, 12, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 2 ).

REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 100.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))

William A. Stein, The modular forms database

Index entries for Molien series

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

FORMULA

a(n) = a(n-2)+a(n-3)-a(n-5). G.f.: (x^4-x^2+1) / ((x-1)^2*(x+1)*(x^2+x+1)). - Colin Barker, Jan 07 2014

a(n) ~ n/6 (first difference is 6-periodic). - Ralf Stephan, Apr 29 2014

a(n) = 2*floor(n/3)-n/2+(3+(-1)^n)/4. - Tani Akinari, Oct 23 2014

MAPLE

(1+x^12)/(1-x^6)/(1-x^8); seq(coeff(series(%, x, 2*n+1), x, 2*n), n=0..100);

MATHEMATICA

CoefficientList[Series[(x^4 - x^2 + 1)/((x - 1)^2 (x + 1) (x^2 + x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 23 2014 *)

PROG

(PARI) Vec((x^4-x^2+1)/((x-1)^2*(x+1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Jan 07 2014

(MAGMA) [2*Floor(n/3)-n/2+(3+(-1)^n)/4: n in [0..100]]; // Vincenzo Librandi, Oct 23 2014

CROSSREFS

Sequence in context: A074746 A133188 A261036 * A029320 A187450 A187449

Adjacent sequences:  A008609 A008610 A008611 * A008613 A008614 A008615

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)