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

5, 11, 35, 131, 515, 2051, 8195, 32771, 131075, 524291, 2097155, 8388611, 33554435, 134217731, 536870915, 2147483651, 8589934595, 34359738371, 137438953475, 549755813891, 2199023255555, 8796093022211, 35184372088835, 140737488355331, 562949953421315, 2251799813685251

Offset: 0

Author

Brad Clardy, Mar 22 2011

Keywords

• nonn
• easy

Comments

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

Number of conjugacy classes in Suzuki group Sz(2*4^n). - Eric M. Schmidt, Apr 18 2013

Examples

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

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Frank Luebeck, Numbers of Conjugacy Classes in Finite Groups of Lie Type.
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A141725 (4^(n+1)-3), A224790.

Programs

Magma

[2*4^n+3: n in [1..100]]; // Vincenzo Librandi, Mar 29 2011
(Decimal BASIC)
FOR n=0 TO 1000
   PRINT n; 2*4^n+3
NEXT n
END ! /* Bruno Berselli, Apr 28 2011 */

Mathematica

2 4^Range[0,30]+3  (* Harvey P. Dale, Apr 02 2011 *)

PARI

a(n)=2*4^n+3 \\ Charles R Greathouse IV, Jul 02 2013

Formula

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

G.f.: (5-14*x)/((1-4*x)*(1-x)). - R. J. Mathar, Apr 09 2011

a(n) = 5*a(n-1) - 4*a(n-2). - Joerg Arndt, Apr 09 2011

From Felix P. Muga II, Mar 19 2014: (Start)

a(n) = a(n-1) + 6*4^(n-1) for n > 0, a(0)=5.

a(n) = a(n-1) + 12*a(n-2) - 36 for n > 1, a(0)=5, a(1)=11. (End)

E.g.f.: exp(x)*(2*exp(3*x) + 3). - Elmo R. Oliveira, Mar 08 2025