A103204 a(1) = 2, a(2) = 4; a(n) = 2*a(n-1) - 1.

2, 4, 7, 13, 25, 49, 97, 193, 385, 769, 1537, 3073, 6145, 12289, 24577, 49153, 98305, 196609, 393217, 786433, 1572865, 3145729, 6291457, 12582913, 25165825, 50331649, 100663297, 201326593, 402653185, 805306369, 1610612737, 3221225473

Offset

1,1

Links

Table of n, a(n) for n=1..32.

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

Formula

a(n) = A003945(n-1) + 1.

a(n) = 3*2^(n-2) + 1 for n>1. - Ralf Stephan, May 18 2007

a(n) = A004119(n-1), n>1. - R. J. Mathar, Jun 11 2010

G.f.: x*(2-2*x-x^2)/(1-3*x+2*x^2). a(n) = 3*a(n-1)-2*a(n-2), n>3. - Colin Barker, Jan 29 2012

Mathematica

a[1] = 2; a[2] = 4; a[n_] := a[n] = 2*a[n - 1] - 1; Table[a[n], {n, 1, 32}]
Join[{2}, NestList[2#-1&, 4, 40]] (* or *) LinearRecurrence[{3, -2}, {2, 4, 7}, 40] (* Harvey P. Dale, Dec 04 2018 *)

Prog

(PARI) Vec(x*(2-2*x-x^2)/(1-3*x+2*x^2) + O(x^50)) \\ Michel Marcus, Jan 29 2016

Crossrefs

Cf. A003945, A004119.

Sequence in context: A176485 A119266 A102026 * A326174 A366109 A017995

Adjacent sequences: A103201 A103202 A103203 * A103205 A103206 A103207

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 19 2005

Status

approved