A199116 a(n) = 6*4^n + 1.

7, 25, 97, 385, 1537, 6145, 24577, 98305, 393217, 1572865, 6291457, 25165825, 100663297, 402653185, 1610612737, 6442450945, 25769803777, 103079215105, 412316860417, 1649267441665, 6597069766657, 26388279066625, 105553116266497, 422212465065985, 1688849860263937

Offset: 0

Author

Vincenzo Librandi, Nov 04 2011

Keywords

• nonn
• easy

Comments

Bisection (odd part) of A181565 and A201630. - Bruno Berselli, Dec 04 2011

First differences of A221130, a(n) = A221130(n+2) - A221130(n+1). - Jaroslav Krizek, Jan 02 2013

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. A140529, A181565, A201630, A221130.

Programs

Magma

[6*4^n+1: n in [0..30]];

Mathematica

6*4^Range[0,30]+1 (* or *) LinearRecurrence[{5,-4},{7,25},30] (* Harvey P. Dale, Apr 18 2024 *)

Formula

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

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

G.f.: (7-10*x)/((1-x)*(1-4*x)). - Bruno Berselli, Nov 04 2011

From Elmo R. Oliveira, May 08 2025: (Start)

E.g.f.: exp(x)*(6*exp(3*x) + 1).

a(n) = A140529(n) + 2. (End)