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 A237036 Size of the smallest conjugacy class of size greater than 1 of the alternating group of degree n. 0
 3, 12, 40, 70, 105, 168, 240, 330, 440, 572, 728, 910, 1120, 1360, 1632, 1938, 2280, 2660, 3080, 3542, 4048, 4600, 5200, 5850, 6552, 7308, 8120, 8990, 9920, 10912, 11968, 13090, 14280, 15540, 16872, 18278, 19760, 21320, 22960, 24682, 26488, 28380, 30360, 32430 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 LINKS Table of n, a(n) for n=4..47. Wikipedia, Alternating group FORMULA From Alois P. Heinz, Feb 04 2014: (Start) G.f.: -x^4*(7*x^8-28*x^7+42*x^6-20*x^5-20*x^4+30*x^3-10*x^2-3)/(x-1)^4. a(n) = 2*C(n,3) = A007290(n) for n>=9. (End) EXAMPLE For n = 4 the conjugacy classes of size greater than 1 of Alt(n) are {(1,2)(3,4), (1,3)(2,4), (1,4)(2,3)}, {(2,4,3), (1,2,3), (1,3,4), (1,4,2)}, {(2,3,4), (1,2,4), (1,3,2), (1,4,3)}, the smallest of which has 3 elements, hence a(4) = 3. MATHEMATICA Join[{3, 12, 40, 70, 105}, 2*Binomial[Range[9, 50], 3]] (* Harvey P. Dale, Apr 07 2018 *) PROG (GAP) a:=function(n) local G, CC, SCC, SCC1; G:=AlternatingGroup(n); CC:=ConjugacyClasses(G);; SCC:=List(CC, Size); SCC1:=Difference(SCC, [1]); return Minimum(SCC1); end;; CROSSREFS Cf. A000702, A070733, A007290. Sequence in context: A271218 A062311 A303348 * A034956 A032093 A007993 Adjacent sequences: A237033 A237034 A237035 * A237037 A237038 A237039 KEYWORD nonn AUTHOR W. Edwin Clark, Feb 02 2014 STATUS approved

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Last modified December 8 08:36 EST 2023. Contains 367663 sequences. (Running on oeis4.)