A198275 a(n) = 17*2^n - 1.
16, 33, 67, 135, 271, 543, 1087, 2175, 4351, 8703, 17407, 34815, 69631, 139263, 278527, 557055, 1114111, 2228223, 4456447, 8912895, 17825791, 35651583, 71303167, 142606335, 285212671, 570425343, 1140850687, 2281701375, 4563402751, 9126805503, 18253611007
Offset: 0
Examples
a(2) = 17*2^2-1 = 67.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Gennady Eremin, Partitioning the set of natural numbers into Mersenne trees and into arithmetic progressions; Natural Matrix and Linnik's constant, arXiv:2405.16143 [math.CO], 2024. See pp. 3, 14.
- Index entries for linear recurrences with constant coefficients, signature (3,-2).
Programs
-
BASIC
for j = 0 to 30 : print str$((17*2^j)-1)+", "; : next j
-
Magma
[17*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011
-
Maple
A198275:=n->17*2^n-1; seq(A198275(n), n=0..30); # Wesley Ivan Hurt, Jun 11 2014
-
Mathematica
17*2^Range[0,30]-1 (* or *) LinearRecurrence[{3,-2},{16,33},40] (* Harvey P. Dale, Dec 03 2011 *)
Formula
a(n+1) = 2*a(n) + 1.
G.f.: ( 16-15*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 25 2011
a(0)=16, a(1)=33, a(n)=3*a(n-1)-2*a(n-2). - Harvey P. Dale, Dec 03 2011
a(n) + a(n-1)^2 = (a(n-1)+1)^2. - Vincenzo Librandi, Jun 11 2014