A153894 - OEIS

%I #43 Oct 09 2023 14:30:01

%S 4,9,19,39,79,159,319,639,1279,2559,5119,10239,20479,40959,81919,

%T 163839,327679,655359,1310719,2621439,5242879,10485759,20971519,

%U 41943039,83886079,167772159,335544319,671088639,1342177279,2684354559

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

%C 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

%C a(n) converted to binary is 100 followed by n ones. - _Alexandre Herrera_, Oct 06 2023

%H Vincenzo Librandi, <a href="/A153894/b153894.txt">Table of n, a(n) for n = 0..1000</a>

%H B. Monjardet, <a href="https://halshs.archives-ouvertes.fr/halshs-00198635">Acyclic domains of linear orders: a survey</a>, 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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

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

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

%F G.f.: (4 - 3*x) / ( (2*x-1)*(x-1) ). - _R. J. Mathar_, Oct 22 2011

%F a(n) + a(n-1)^2 = A309779(n), a perfect square. - _Vincenzo Librandi_, Oct 28 2011

%F From _G. C. Greubel_, Sep 01 2016: (Start)

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

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

%t a=4;lst={a};Do[a=a*2+1;AppendTo[lst,a],{n,5!}];lst

%t LinearRecurrence[{3,-2},{4,9}, 25] (* or *) Table[5*2^n - 1, {n,0,25}] (* _G. C. Greubel_, Sep 01 2016 *)

%o (Magma) [5*2^n-1: n in [0..30]]; // _Vincenzo Librandi_, Oct 28 2011

%o (PARI) a(n)=5*2^n-1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A052549, A309779.

%K nonn,easy

%O 0,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 03 2009

%E Edited by _N. J. A. Sloane_, Feb 07 2009

%E Definition corrected by _Franklin T. Adams-Watters_, Apr 22 2009