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%I #11 Sep 28 2016 07:52:56
%S 1512,10073444472,49825657439340552,239189910264352349332632,
%T 1144503123693984541835958820392,
%U 5474370186265837734230137135972625592,26183874281059869023477124043633901590825032,125236728809915185354190019796969393286848248539352,599003428666412716882958241970105468686115269921659258472
%N Order of twisted group 2G2(3^(2*n + 1)).
%D R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14.
%D 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.
%H Harry J. Smith, <a href="/A064584/b064584.txt">Table of n, a(n) for n=0,...,50</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5321700,-2580612660198,18555620546801700,-12157665459056928801).
%F a(n) = q^6*(q^2-1)*(q^6+1), where q^2 = 3^(2*n+1).
%F G.f.: 1512*(1+59049*x)*(1+1281582*x+3486784401*x^2) / ((1-729*x)*(1-6561*x)*(1-531441*x)*(1-4782969*x)). - _Colin Barker_, Dec 25 2015
%t LinearRecurrence[{5321700,-2580612660198,18555620546801700,-12157665459056928801},{1512,10073444472,49825657439340552,239189910264352349332632},10] (* _Harvey P. Dale_, Sep 28 2016 *)
%o (PARI) { for (n=0, 50, q2 = 3^(2*n + 1); a=q2^3*(q2 - 1)*(q2^3 + 1); write("b064584.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 19 2009
%o (PARI) Vec(1512*(1+59049*x)*(1+1281582*x+3486784401*x^2) / ((1-729*x)*(1-6561*x)*(1-531441*x)*(1-4782969*x)) + O(x^10)) \\ _Colin Barker_, Dec 25 2015
%Y Cf. A033669, A037251.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Oct 17 2001
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