|
Search: id:A070953
|
|
|
| A070953 |
|
Order of the group GU(n,2), the general unitary n X n matrices over the finite field GF(4). |
|
+0
1
|
|
| 3, 18, 648, 77760, 41057280, 82771476480, 683361309818880, 22304913152488243200, 2929259634489976002969600, 1534275894314621670931405209600, 3219180858829475639028172057057689600
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Replacing 2 in the definition by a prime power q, the order of the group GU(n,q), the general unitary n X n matrices over the finite field GF(q^2) is (q+1) * q^(n(n-1)/2) * product i=1..(n-1) (q^(i+1) - (-1)^(i+1)).
|
|
REFERENCES
|
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups, Oxford Univ. Press, 1985.
|
|
FORMULA
|
For n>=2 a(n) = 3 * 2^(n(n-1)/2) * product i=1..(n-1) (2^(i+1) - (-1)^(i+1))
|
|
PROGRAM
|
(PARI) for(n=2, 30, print1( 3*2^(n*(n-1)/2)*prod(i=1, (n-1), (2^(i+1)-(-1)^(i+1))), ", "))
|
|
CROSSREFS
|
Sequence in context: A083000 A118704 A132514 this_sequence A064846 A000853 A065402
Adjacent sequences: A070950 A070951 A070952 this_sequence A070954 A070955 A070956
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Sharon Sela (sharonsela(AT)hotmail.com), May 24 2002
|
|
EXTENSIONS
|
More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 06 2002
|
|
|
Search completed in 0.002 seconds
|
