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

a(n) = floor((n^2+17*n+144)/336 + n*(-1)^n/48 + ((n^2+3*n+4) mod 7)/7). - Hoang Xuan Thanh, Sep 09 2025

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 *)

Prog

(PARI) a(n) = (n^2+17*n+144 + 7*n*(-1)^n + 48*((n^2+3*n+4)%7))\336 \\ Hoang Xuan Thanh, Sep 09 2025

Crossrefs

Sequence in context: A376798 A388722 A185318 * A029414 A053275 A025816

Adjacent sequences: A008619 A008620 A008621 * A008623 A008624 A008625

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved