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A064487
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Order of twisted Suzuki group Sz(2^(2*n + 1)), also known as the group 2B2(2^(2*n + 1)).
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4
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20, 29120, 32537600, 34093383680, 35115786567680, 36011213418659840, 36888985097480437760, 37777778976635853209600, 38685331082014736871587840, 39614005699412557795646504960, 40564799864499450381466515537920
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OFFSET
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0,1
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COMMENTS
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For n >= 3, a(n) has at least 5 distinct prime factors. See my link for a proof. - Jianing Song, Apr 04 2022
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REFERENCES
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R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14.
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LINKS
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J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985, p. xvi. See ATLAS v. 3
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FORMULA
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a(n) = q^4*(q^2-1)*(q^4+1), where q^2 = 2^(2*n+1).
G.f.: 20*(1+128*x)*(1-32*x+16384*x^2) / ((1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)). - Colin Barker, Dec 25 2015
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MATHEMATICA
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LinearRecurrence[{1360, -365568, 22282240, -268435456}, {20, 29120, 32537600, 34093383680}, 20] (* Harvey P. Dale, Sep 08 2018 *)
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PROG
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(GAP) g := Sz(32); s := Size(g);
(Magma) [ #Sz(2^(2*n+1)) : n in [0..10]]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
(PARI) Vec(20*(1+128*x)*(1-32*x+16384*x^2)/((1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)) + O(x^20)) \\ Colin Barker, Dec 25 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Oct 15 2001
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STATUS
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approved
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