A198693 a(n) = 3*4^n-1.

2, 11, 47, 191, 767, 3071, 12287, 49151, 196607, 786431, 3145727, 12582911, 50331647, 201326591, 805306367, 3221225471, 12884901887, 51539607551, 206158430207, 824633720831, 3298534883327, 13194139533311, 52776558133247

Offset: 0

Author

Vincenzo Librandi, Oct 29 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A024036, A097743, A114569, A156760.

Programs

Magma

[3*4^n-1: n in [0..30]]

Mathematica

3*4^Range[0,30]-1 (* or *) LinearRecurrence[{5,-4},{2,11},30] (* Harvey P. Dale, Jul 04 2017 *)

Formula

a(n) = 4*a(n-1)+3.

a(n) = 5*a(n-1) - 4*a(n-2), for n > 1.

G.f.: (2+x)/((4*x-1)*(x-1)). - R. J. Mathar, Oct 30 2011