A198276 a(n) = 19*2^n-1.
18, 37, 75, 151, 303, 607, 1215, 2431, 4863, 9727, 19455, 38911, 77823, 155647, 311295, 622591, 1245183, 2490367, 4980735, 9961471, 19922943, 39845887, 79691775, 159383551, 318767103, 637534207, 1275068415, 2550136831, 5100273663, 10200547327, 20401094655
Offset: 0
Examples
a(2) = 19*2^2-1 = 75.
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
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BASIC
for j = 0 to 30 : print str$((19*2^j)-1)+", "; : next j
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Magma
[19*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011
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Maple
A198276:=n->19*2^n-1; seq(A198276(n), n=0..30); # Wesley Ivan Hurt, Jun 11 2014
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Mathematica
19*2^Range[0,30]-1 (* or *) LinearRecurrence[{3,-2},{18,37},40] (* Harvey P. Dale, Dec 18 2013 *)
Formula
a(n+1) = 2*a(n) + 1.
G.f.: ( 18-17*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 25 2011
a(n) + a(n-1)^2 = (a(n-1)+1)^2. - Vincenzo Librandi, Jun 11 2014