A008622 Expansion of 1/((1-x^4)*(1-x^6)*(1-x^7)).

1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 2, 4, 3, 4, 3, 5, 3, 5, 4, 6, 4, 6, 5, 7, 5, 7, 6, 8, 6, 9, 7, 9, 7, 10, 8, 11, 9, 11, 9, 12, 10, 13, 11, 14, 11, 14, 12, 16, 13, 16, 14, 17, 14, 18, 16, 19, 16, 20, 17, 21, 18, 22, 19, 23, 20, 24, 21, 25, 22, 26, 23, 28, 24, 28

Offset

0,13

Comments

Molien series of 3-dimensional representation of GL(3,2) over GF(2).

References

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 106.

Links

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

A. Adem, Recent developments in the cohomology of finite groups, Notices Amer. Math. Soc., 44 (1997), 806-812.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 231

Index entries for Molien series

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

Formula

a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=0, a(6)=1, a(7)=1, a(8)=1, a(9)=0, a(10)=1, a(11)=1, a(12)=2, a(13)=1, a(14)=2, a(15)=1, a(16)=2, a(n)=a(n-4)+a(n-6)+a(n-7)-a(n-10)-a(n-11)-a(n-13)+a(n-17). - Harvey P. Dale, May 09 2013

a(n) ~ 1/336*n^2. - Ralf Stephan, Apr 29 2014

Maple

1/(1-x^4)/(1-x^6)/(1-x^7);

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^6)(1-x^7)), {x, 0, 90}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 0, 1, 1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 2}, 90] (* Harvey P. Dale, May 09 2013 *)

Crossrefs

Sequence in context: A176725 A085029 A185318 * A029414 A053275 A025816

Adjacent sequences: A008619 A008620 A008621 * A008623 A008624 A008625

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved