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
Vincenzo Librandi, Table of n, a(n) for n = 0..200
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
KEYWORD
nonn,easy
AUTHOR
Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Oct 15 2001
STATUS
approved