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 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 Table of n, a(n) for n=1..55. 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). Index entries for sequences related to groups 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 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 Missing zero in the row for A_9 inserted by N. J. A. Sloane, Mar 27 2015 STATUS approved

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