|
| |
|
|
A008670
|
|
Molien series for Weyl group F_4.
|
|
1
| |
|
|
1, 1, 1, 2, 3, 3, 5, 6, 7, 9, 11, 12, 16, 18, 20, 24, 28, 30, 36, 40, 44, 50, 56, 60, 69, 75, 81, 90, 99, 105, 117, 126, 135, 147, 159, 168, 184, 196, 208, 224, 240, 252, 272, 288, 304, 324, 344, 360, 385, 405, 425, 450, 475, 495, 525, 550, 575, 605, 635, 660, 696, 726, 756
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
REFERENCES
| Coxeter and Moser, Gens. and Relations for Discrete Grps, Table 10.
L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 28).
|
|
|
LINKS
| G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 236
Index entries for Molien series
|
|
|
FORMULA
| G.f. 1/((1-x^2)*(1-x^6)*(1-x^8)*(1-x^12)).
a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=3, a(6)=5, a(7)=6, a(8)=7, a(9)=9, a(10)=11, a(11)=12, a(12)=16, a(13)=18, a(n)=a(n-1)+a(n-3)- a(n-5)+ a(n-6)-2*a(n-7)+a(n-8)-a(n-9)+a(n-11)+a(n-13)-a(n-14) [From Harvey P. Dale, Feb 07 2012]
|
|
|
MAPLE
| a:= proc(n) local m, r; m := iquo (n, 12, 'r'); r:= r+1; ([4, 5, 6, 8, 10, 11, 14, 16, 18, 21, 24, 26][r]+ (6+r+4*m)*m)*m+ [1$3, 2, 3$2, 5, 6, 7, 9, 11, 12][r] end: seq (a(n), n=0..100); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 06 2008]
|
|
|
MATHEMATICA
| Take[CoefficientList[Series[1/((1-x^2)(1-x^6)(1-x^8)(1-x^12)), {x, 0, 130}], x], {1, -1, 2}] (* or *) LinearRecurrence[ {1, 0, 1, 0, -1, 1, -2, 1, -1, 0, 1, 0, 1, -1}, {1, 1, 1, 2, 3, 3, 5, 6, 7, 9, 11, 12, 16, 18}, 70] (* From Harvey P. Dale, Feb 07 2012 *)
|
|
|
PROG
| (MAGMA) MolienSeries(CoxeterGroup("F4")); - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
|
|
|
CROSSREFS
| Sequence in context: A081210 A070321 A036410 * A193748 A039852 A035938
Adjacent sequences: A008667 A008668 A008669 * A008671 A008672 A008673
|
|
|
KEYWORD
| nonn,easy,nice,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
