A153894 a(n) = 5*2^n - 1.

4, 9, 19, 39, 79, 159, 319, 639, 1279, 2559, 5119, 10239, 20479, 40959, 81919, 163839, 327679, 655359, 1310719, 2621439, 5242879, 10485759, 20971519, 41943039, 83886079, 167772159, 335544319, 671088639, 1342177279, 2684354559

Offset

0,1

Comments

a(n) is the total number of symbols required in the fully-expanded von Neumann definition of ordinal n + 1, where the string "{}" is used to represent the empty set and spaces are ignored. - Ely Golden, Nov 14 2019

a(n) converted to binary is 100 followed by n ones. - Alexandre Herrera, Oct 06 2023

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

B. Monjardet, Acyclic domains of linear orders: a survey, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139-160. This version: <halshs-00198635>. - N. J. A. Sloane, Feb 07 2009

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

Formula

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

a(n) = A052549(n+1).

G.f.: (4 - 3*x) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 22 2011

a(n) + a(n-1)^2 = A309779(n), a perfect square. - Vincenzo Librandi, Oct 28 2011

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

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

E.g.f.: 5*exp(2*x) - exp(x). (End)

Mathematica

a=4; lst={a}; Do[a=a*2+1; AppendTo[lst, a], {n, 5!}]; lst
LinearRecurrence[{3, -2}, {4, 9}, 25] (* or *) Table[5*2^n - 1, {n, 0, 25}] (* G. C. Greubel, Sep 01 2016 *)

Prog

(Magma) [5*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011
(PARI) a(n)=5*2^n-1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A052549, A309779.

Sequence in context: A008135 A009885 A052549 * A301137 A214318 A300438

Adjacent sequences: A153891 A153892 A153893 * A153895 A153896 A153897

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 03 2009

Extensions

Edited by N. J. A. Sloane, Feb 07 2009

Definition corrected by Franklin T. Adams-Watters, Apr 22 2009

Status

approved