login
a(n) = 2*4^n + 3.
15

%I #53 Mar 28 2024 13:18:53

%S 5,11,35,131,515,2051,8195,32771,131075,524291,2097155,8388611,

%T 33554435,134217731,536870915,2147483651,8589934595,34359738371,

%U 137438953475,549755813891,2199023255555,8796093022211,35184372088835,140737488355331

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

%C For n > 0, binary representation of a(n) is 1X11 where X is 2*n-1 zeros.

%C Number of conjugacy classes in Suzuki group Sz(2*4^n). - _Eric M. Schmidt_, Apr 18 2013

%H Bruno Berselli, <a href="/A188161/b188161.txt">Table of n, a(n) for n = 0..1000</a>

%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).

%F a(n) = A141725(n) - 2*A141725(n-1) for n > 0.

%F G.f. ( 5-14*x ) / ( (1-4*x)*(1-x) ). - _R. J. Mathar_, Apr 09 2011

%F a(n) = +5*a(n-1) -4*a(n-2). [_Joerg Arndt_, Apr 09 2011]

%F a(n) = a(n-1)+6*4^(n-1) for n > 0, a(0)=5. - _Felix P. Muga II_, Mar 19 2014

%F a(n) = a(n-1)+12*a(n-2)-36 for n > 1, a(0)=5, a(1)=11. - _Felix P. Muga II_, Mar 19 2014

%e The first seven terms written in binary are 101, 1011, 100011, 10000011, 1000000011, 100000000011, and 10000000000011.

%t 2 4^Range[0,30]+3 (* _Harvey P. Dale_, Apr 02 2011 *)

%o (Magma) [2*4^n+3: n in [1..100]]; // _Vincenzo Librandi_, Mar 29 2011

%o (Decimal BASIC)

%o FOR n=0 TO 1000

%o PRINT n; 2*4^n+3

%o NEXT n

%o END ! /* _Bruno Berselli_, Apr 28 2011 */

%o (PARI) a(n)=2*4^n+3 \\ _Charles R Greathouse IV_, Jul 02 2013

%Y Cf. A141725: 4^(n+1)-3; A224790.

%K nonn,easy

%O 0,1

%A _Brad Clardy_, Mar 22 2011