0,1

A020944(a(n)) = 0. - Reinhard Zumkeller, Mar 13 2011

a(n) + a(n-1)^2 is a perfect square. - Vincenzo Librandi, Oct 28 2011

Number of distinct continued fractions of n terms chosen from {1,2}. - Clark Kimberling, Jul 20 2015

Also, the decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 643", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. See A283508. - Robert Price, Mar 09 2017

This sequence has been used by the ninth-century mathematician Thabit ibn Qurra to devise the first method to construct amicable pairs (see Tattersall). - Stefano Spezia, Jul 18 2025

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 138.

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. 2-5, 14.

Gennady Eremin, Infinite matrix of odd natural numbers. A bit about Sophie Germain prime numbers, arXiv:2501.17090 [math.GM], 2025. See pp. 3, 11.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

a(n) = a(n-1)*2 + 1, a(0)=2.

a(n) = A083329(n+1).

a(n) = A055010(n+1).

G.f.: (2 - x)/((1-x)(1-2x)). - R. J. Mathar, Feb 13 2009

a(n) = A083416(2n) = A033484(n) + 1. - Philippe Deléham, Apr 14 2013

From G. C. Greubel, Sep 01 2016: (Start)

a(n) = 3*a(n-1) - 2*a(n-2).

E.g.f.: 3*exp(2*x) - exp(x). (End)

Table[3*2^n - 1 , {n, 0, 25}] (* G. C. Greubel, Sep 01 2016 *)

LinearRecurrence[{3, -2}, {2, 5}, 40] (* Harvey P. Dale, Mar 01 2024 *)

(Magma) [3*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011

(PARI) a(n)=3*2^n-1 \\ Charles R Greathouse IV, Sep 24 2015

Cf. A283508.

Essentially the same as A052940.

Sequence in context: A133489 A060153 A086219 * A083329 A055010 A266550

Adjacent sequences: A153890 A153891 A153892 * A153894 A153895 A153896

nonn,easy

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Edited by N. J. A. Sloane, Feb 14 2009

approved