login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057740 Irregular triangle read by rows: T(n,k) is the number of elements of alternating group A_n having order k, for n >= 1, 1 <= k <= A051593(n). 11
1, 1, 1, 0, 2, 1, 3, 8, 1, 15, 20, 0, 24, 1, 45, 80, 90, 144, 1, 105, 350, 630, 504, 210, 720, 1, 315, 1232, 3780, 1344, 5040, 5760, 0, 0, 0, 0, 0, 0, 0, 2688, 1, 1323, 5768, 18900, 3024, 37800, 25920, 0, 40320, 9072, 0, 15120, 0, 0, 24192 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
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.
LINKS
Koda, Tatsuhiko; Sato, Masaki; Takegahara, Yugen; 2-adic properties for the numbers of involutions in the alternating groups, J. Algebra Appl. 14 (2015), no. 4, 1550052 (21 pages).
EXAMPLE
Triangle begins:
1;
1;
1, 0, 2;
1, 3, 8;
1, 15, 20, 0, 24;
1, 45, 80, 90, 144;
1, 105, 350, 630, 504, 210, 720;
1, 315, 1232, 3780, 1344, 5040, 5760, 0, 0, 0, 0, 0, 0, 0, 2688;
1, 1323, 5768, 18900, 3024, 37800, 25920, 0, 40320, 9072, 0, 15120, 0, 0, 24192;
...
MATHEMATICA
row[n_] := (orders = PermutationOrder /@ GroupElements[AlternatingGroup[n] ]; Table[Count[orders, k], {k, 1, Max[orders]}]); Table[row[n], {n, 1, 9}] // Flatten (* Jean-François Alcover, Aug 31 2016 *)
PROG
(Magma) {* Order(g) : g in Alt(6) *};
CROSSREFS
Column 2, 3, 4 are A048099, A001471, A051695.
Sequence in context: A135299 A092081 A203997 * A320875 A265891 A248354
KEYWORD
nonn,tabf,easy,nice
AUTHOR
Roger Cuculière, Oct 29 2000
EXTENSIONS
More terms from N. J. A. Sloane, Nov 01 2000
Missing zero in the row for A_9 inserted by N. J. A. Sloane, Mar 27 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 3 12:51 EST 2024. Contains 370512 sequences. (Running on oeis4.)