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A188161 a(n) = 2*4^n + 3.

%I A188161 #56 Mar 08 2025 17:16:07
%S A188161 5,11,35,131,515,2051,8195,32771,131075,524291,2097155,8388611,
%T A188161 33554435,134217731,536870915,2147483651,8589934595,34359738371,
%U A188161 137438953475,549755813891,2199023255555,8796093022211,35184372088835,140737488355331,562949953421315,2251799813685251
%N A188161 a(n) = 2*4^n + 3.
%C A188161 For n > 0, binary representation of a(n) is 1X11 where X is 2*n-1 zeros.
%C A188161 Number of conjugacy classes in Suzuki group Sz(2*4^n). - _Eric M. Schmidt_, Apr 18 2013
%H A188161 Bruno Berselli, <a href="/A188161/b188161.txt">Table of n, a(n) for n = 0..1000</a>
%H A188161 Frank Luebeck, <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/nrclasses/nrclasses.html">Numbers of Conjugacy Classes in Finite Groups of Lie Type</a>.
%H A188161 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F A188161 a(n) = A141725(n) - 2*A141725(n-1) for n > 0.
%F A188161 G.f.: (5-14*x)/((1-4*x)*(1-x)). - _R. J. Mathar_, Apr 09 2011
%F A188161 a(n) = 5*a(n-1) - 4*a(n-2). - _Joerg Arndt_, Apr 09 2011
%F A188161 From _Felix P. Muga II_, Mar 19 2014: (Start)
%F A188161 a(n) = a(n-1) + 6*4^(n-1) for n > 0, a(0)=5.
%F A188161 a(n) = a(n-1) + 12*a(n-2) - 36 for n > 1, a(0)=5, a(1)=11. (End)
%F A188161 E.g.f.: exp(x)*(2*exp(3*x) + 3). - _Elmo R. Oliveira_, Mar 08 2025
%e A188161 The first seven terms written in binary are 101, 1011, 100011, 10000011, 1000000011, 100000000011, and 10000000000011.
%t A188161 2 4^Range[0,30]+3  (* _Harvey P. Dale_, Apr 02 2011 *)
%o A188161 (Magma) [2*4^n+3: n in [1..100]]; // _Vincenzo Librandi_, Mar 29 2011
%o A188161 (Decimal BASIC)
%o A188161 FOR n=0 TO 1000
%o A188161    PRINT n; 2*4^n+3
%o A188161 NEXT n
%o A188161 END ! /* _Bruno Berselli_, Apr 28 2011 */
%o A188161 (PARI) a(n)=2*4^n+3 \\ _Charles R Greathouse IV_, Jul 02 2013
%Y A188161 Cf. A141725 (4^(n+1)-3), A224790.
%K A188161 nonn,easy
%O A188161 0,1
%A A188161 _Brad Clardy_, Mar 22 2011