login
A064487
Order of twisted Suzuki group Sz(2^(2*n + 1)), also known as the group 2B2(2^(2*n + 1)).
4
20, 29120, 32537600, 34093383680, 35115786567680, 36011213418659840, 36888985097480437760, 37777778976635853209600, 38685331082014736871587840, 39614005699412557795646504960, 40564799864499450381466515537920
OFFSET
0,1
COMMENTS
Every term in A056866 is divisible by 12 or 20. Those terms that are not divisible by 12 are divisible by a term from this sequence. - Charles R Greathouse IV via Danny Rorabaugh, Apr 21 2015
For n >= 3, a(n) has at least 5 distinct prime factors. See my link for a proof. - Jianing Song, Apr 04 2022
REFERENCES
R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14.
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
LINKS
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi. See ATLAS v. 3
Michio Suzuki, A new type of simple groups of finite order, Proc Natl Acad Sci U S A. 46:6 (1960), pp. 868-870.
Index entries for linear recurrences with constant coefficients, signature (1360,-365568,22282240,-268435456).
FORMULA
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
MATHEMATICA
LinearRecurrence[{1360, -365568, 22282240, -268435456}, {20, 29120, 32537600, 34093383680}, 20] (* Harvey P. Dale, Sep 08 2018 *)
PROG
(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) a(n)=my(t=2^(2*n+1)); t^2*(t-1)*(t^2+1) \\ Charles R Greathouse IV, Apr 21 2015
(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
CROSSREFS
Cf. A037250, A064583. A257391 is a subsequence.
Sequence in context: A348144 A060618 A369948 * A099187 A129041 A129040
KEYWORD
nonn,easy
AUTHOR
Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Oct 15 2001
STATUS
approved