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A057740 Irregular triangle read by rows: T(n,k) = 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.

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).

LINKS

Table of n, a(n) for n=1..55.

Index entries for sequences related to groups

EXAMPLE

1; 1; 1,0,2; 1,3,8; 1,15,20,0,24; ...

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,

1, 5355, 31040, 94500, 78624, 201600, 86400, 226800, 403200, 90720, 0, 302400, 0. 0, 120960, 0, 0, 0, 0, 0, 172800

...

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

Cf. A057731 (S_n), A054522, A057741, A051593, A000793.

Column 2, 3, 4 are A048099, A001471, A051695.

See also A061129, A061130, A061131, A061132, A061133, A061134, A061135, A061136, A061137, A061138, A061139, A061140.

Sequence in context: A135299 A092081 A203997 * A320875 A265891 A248354

Adjacent sequences:  A057737 A057738 A057739 * A057741 A057742 A057743

KEYWORD

nonn,tabf,easy,nice

AUTHOR

Roger Cuculière, Oct 29 2000

EXTENSIONS

More terms from N. J. A. Sloane, Nov 01 2000

Inserted missing zero in the row for A_9. - N. J. A. Sloane, Mar 27 2015

STATUS

approved

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Last modified February 25 05:01 EST 2020. Contains 332217 sequences. (Running on oeis4.)