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

Author

Roger L. Bagula, Mar 19 2005

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A003945, A004119.

Programs

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 *)

PARI

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

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