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A153894
a(n) = 5*2^n - 1.
16
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
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
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
Sequence in context: A008135 A009885 A052549 * A372448 A301137 A214318
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Feb 07 2009
Definition corrected by Franklin T. Adams-Watters, Apr 22 2009
STATUS
approved