A196305 a(n) = 15*2^n - 1.

14, 29, 59, 119, 239, 479, 959, 1919, 3839, 7679, 15359, 30719, 61439, 122879, 245759, 491519, 983039, 1966079, 3932159, 7864319, 15728639, 31457279, 62914559, 125829119, 251658239, 503316479, 1006632959, 2013265919, 4026531839, 8053063679, 16106127359, 32212254719, 64424509439

Offset: 0

Author

Brad Clardy, Oct 07 2011

Keywords

• nonn
• easy

Comments

Primes of this sequence are in A196940.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• 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).

Crossrefs

Cf. A033484, A083705, A110286 (first differences), A196940.

Programs

Magma

[15*2^n -1 : n in [0..50]];

PARI

a(n)=15<Charles R Greathouse IV, Oct 08 2011

Formula

a(n) = 15*2^n - 1.

a(n) = A033484(n+1) + A083705(n).

From Philippe Deléham, Feb 17 2014: (Start)

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

a(n) = 3*a(n-2) - 2*a(n-2).

a(n) = A110286(n) - 1. (End)

From Elmo R. Oliveira, Sep 14 2024: (Start)

G.f.: (14 - 13*x)/((1 - x)*(1 - 2*x)).

E.g.f.: exp(x)*(15*exp(x) - 1). (End)