|
Search: id:A008614
|
|
|
| A008614 |
|
Molien series of 3-dimensional representation of group GL(3,2) = L(2,7) of order 168. |
|
+0
1
|
|
| 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 3, 0, 3, 1, 3, 0, 4, 1, 4, 1, 5, 1, 5, 1, 6, 2, 6, 2, 7, 2, 7, 3, 8, 3, 9, 3, 9, 4, 10, 4, 11, 5, 11, 5, 12, 6, 13, 6, 14, 7, 14, 7, 16, 8, 16, 9, 17, 9, 18, 10, 19, 11, 20, 11, 21, 12, 22, 13, 23, 14, 24, 14, 25, 16, 26, 16, 28, 17, 28, 18, 30
(list; graph; listen)
|
|
|
OFFSET
|
0,13
|
|
|
REFERENCES
|
D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 101.
T. A. Springer, Invariant Theory, Lecture Notes in Math., Vol. 585, Springer, p. 97.
|
|
LINKS
|
Index entries for Molien series
|
|
FORMULA
|
Euler transform of length 42 sequence [ 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]. - Michael Somos Oct 11 2006
G.f.: (1-x^42)/((1-x^4)*(1-x^6)*(1-x^14)*(1-x^21)). a(-3-n)=a(n). a(n)=a(n-4)+a(n-6)-a(n-10)+a(n-14)-a(n-18)-a(n-20)+a(n-24). - Michael Somos Oct 11 2006
|
|
MAPLE
|
(1+x^21)/(1-x^4)/(1-x^6)/(1-x^14);
|
|
PROGRAM
|
(PARI) {a(n)=if(n%2, n-=21); n/=2; if(n<-11, n=-12-n); polcoeff( 1/(1-x^2)/(1-x^3)/(1-x^7)+x*O(x^n), n)} /* Michael Somos Oct 11 2006 */
|
|
CROSSREFS
|
Cf. a(2n+21)=a(2n)=A008671(n).
Sequence in context: A096158 A053471 A144078 this_sequence A036663 A096577 A137899
Adjacent sequences: A008611 A008612 A008613 this_sequence A008615 A008616 A008617
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
