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A153894 a(n) = 5*2^n - 1. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

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

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 * A214318 A034479 A183304

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

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Last modified November 22 08:57 EST 2017. Contains 295076 sequences.