A086225 a(n) = 11*2^n - 1.

10, 21, 43, 87, 175, 351, 703, 1407, 2815, 5631, 11263, 22527, 45055, 90111, 180223, 360447, 720895, 1441791, 2883583, 5767167, 11534335, 23068671, 46137343, 92274687, 184549375, 369098751, 738197503, 1476395007, 2952790015

Offset: 0

Author

Marco Matosic, Jul 29 2003

Keywords

• nonn
• easy

Comments

(a(n-1))^2 + a(n) is a square. - Vincenzo Librandi, Aug 08 2010

Links

• Harvey P. Dale, 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. 3-4.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A000079, A005015.

Programs

Mathematica

NestList[2#+1&,10,30] (* or *) LinearRecurrence[{3,-2},{10,21},30] (* Harvey P. Dale, Nov 25 2013 *)

PARI

a(n) = 11*2^n - 1 \\ Michel Marcus, Jul 15 2013

Formula

a(n) = 2*a(n-1) + 1.

G.f.: (10 - 9*x)/((2*x - 1)*(x - 1)). - R. J. Mathar, Oct 22 2011

E.g.f.: exp(x)*(11*exp(x) - 1). - Stefano Spezia, May 05 2025