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A090492 G.f.: (1+x^10)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)). 1
1, 0, 1, 1, 2, 2, 3, 3, 5, 5, 8, 7, 11, 11, 15, 16, 20, 21, 27, 28, 35, 36, 44, 46, 55, 58, 67, 71, 82, 86, 99, 103, 117, 123, 138, 145, 161, 169, 187, 196, 216, 225, 247, 258, 281, 294, 318, 332, 359, 374, 403, 419, 450, 468, 501, 521, 555, 577, 614, 637, 677, 701, 743, 770, 814 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A_8 = SL_2(4) and acts on F_2[x_1, ..., x_4]. There are two copies of A_5 inside A_8. This is the Poincare series (or Molien series) for the subgroup A_5 acting on F_2[x_1, ..., x_4] by tensoring over F_2 from the action of S_5 on Z^4 where Z^4 consists of those elements (n_1, ..., n_5) with Sum n_i = 0. That is, A_5 acts on the sub-ring F_2[x_1 - x_5, x_2 - x_5, x_3 - x_5, x_4 - x_5] subset F_2[x_1, ..., x_5] by restriction to A_5 of the permutation S_5 action. See A089596 for the other A_5.

REFERENCES

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 113.

H. Derksen and G. Kemper, Computational Invariant Theory, Springer, 2002; p. 130.

LINKS

Table of n, a(n) for n=0..64.

Index entries for Molien series

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

FORMULA

a(n) ~ 1/360*n^3 + 1/60*n^2. - Ralf Stephan, Apr 29 2014

G.f.: ( 1-x^2-x^6+x^4+x^8 ) / ( (1+x+x^2)*(1+x+x^3+x^2+x^4)*(1+x)^2*(x-1)^4 ). - R. J. Mathar, Dec 18 2014

Euler transform of length 20 sequence [ 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]. - Michael Somos, Jul 19 2015

a(n) = - a(-4-n) for all n in Z. - Michael Somos, Jul 19 2015

EXAMPLE

G.f. = 1 + x^2 + x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 5*x^8 + 5*x^9 + ...

PROG

(PARI) {a(n) = (n^3 + 6*n^2 + 96*n - 45*(n%2)*(n+2) - 9*(n%15==11)) \ 360 + 1}; /* Michael Somos, Jul 19 2015 */

(PARI) {a(n) = my(s=1); if( n<0, n = -4-n; s = -1); s * polcoeff( (1 + x^10) / ((1 - x^2) * (1 - x^3) * (1 - x^4) * (1 - x^5)) + x * O(x^n), n)}; /* Michael Somos, Jul 19 2015 */

(PARI) Vec((1+x^10)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)) + O(x^80)) \\ Michel Marcus, Jul 19 2015

CROSSREFS

Sequence in context: A116575 A244800 A275972 * A239949 A103609 A237800

Adjacent sequences:  A090489 A090490 A090491 * A090493 A090494 A090495

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 02 2004

STATUS

approved

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Last modified December 9 23:16 EST 2016. Contains 278993 sequences.