A122041 a(n) = 2*a(n-1) - 1 for n>1, a(1)=23.

23, 45, 89, 177, 353, 705, 1409, 2817, 5633, 11265, 22529, 45057, 90113, 180225, 360449, 720897, 1441793, 2883585, 5767169, 11534337, 23068673, 46137345, 92274689, 184549377, 369098753, 738197505, 1476395009, 2952790017

Offset: 1

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 14 2006

Keywords

• nonn

Comments

From a quiz.

Examples

			23x2 -1 = 45; 45x2 -1 = 89; 89x2 -1 = 177; 2x177 -1 = 353.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Programs

GAP

List([1..30], n-> 1 + 11*2^n); # G. C. Greubel, Oct 04 2019

Magma

[1+11*2^n: n in [1..30]]; // G. C. Greubel, Oct 04 2019

Maple

seq(1 + 11*2^n, n=1..30); # G. C. Greubel, Oct 04 2019

Mathematica

NestList[2#-1&,23,30] (* or *) LinearRecurrence[{3,-2},{23,45},30] (* Harvey P. Dale, Dec 13 2012 *)

PARI

a(n)=if(n>1,2*a(n-1)-1,23); for(n=1,40,print1(a(n),","))

Sage

[1+11*2^n for n in (1..30)] # G. C. Greubel, Oct 04 2019

Formula

a(n) = A083683(n). - R. J. Mathar, Aug 02 2008

a(n) = 11*2^n + 1 for n>=1. - Paolo P. Lava, Oct 01 2008

a(n) = 3*a(n-1) - 2*a(n-2), a(1)=23, a(2)=45. - Harvey P. Dale, Dec 13 2012

From G. C. Greubel, Oct 04 2019: (Start)

G.f.: x*(23 - 24*x)/((1-x)*(1-2*x)).

E.g.f.: 11*exp(2*x) + exp(x) - 12. (End)