|
Search: id:A060840
|
|
|
| A060840 |
|
Number of irreducible representations of symmetric group S_n whose degree is not divisible by 3. |
|
+0
2
|
|
| 1, 2, 3, 3, 6, 9, 9, 18, 9, 9, 18, 27, 27, 54, 81, 81, 162, 54, 54, 108, 162, 162, 324, 486, 486, 972, 27, 27, 54, 81, 81, 162, 243, 243, 486, 243, 243, 486, 729, 729, 1458, 2187, 2187, 4374, 1458, 1458, 2916, 4374, 4374, 8748, 13122, 13122, 26244, 405, 405, 810
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
I. G. MacDonald, On the degrees of the irreducible representations of symmetric groups, Bull. London Math. Soc. 3 (1971), 189-192
|
|
FORMULA
|
If n = sum a_i*3^e[i] in base 3 where a_i is 0, 1, 2 then a(n) = product g(i) where if a(i) = 0 g(i) = 1, if a(i) = 1 g(i) = 3^i, if a(i) = 2 g(i) = 3^i * (3^i + 3) / 2
|
|
EXAMPLE
|
a(4) = 3 because the degrees for S_4 are 1,1,2,3,3 and by the formula: 4 in base 3 is 11 and a(4) = 1*3
|
|
CROSSREFS
|
A059867.
Adjacent sequences: A060837 A060838 A060839 this_sequence A060841 A060842 A060843
Sequence in context: A027037 A020878 A027100 this_sequence A074717 A129068 A079888
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Noam Katz (noamkj(AT)hotmail.com), May 02 2001
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), May 10 2001
|
|
|
Search completed in 0.002 seconds
|
