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
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