A135440 a(n) = a(n-1) + 2a(n-2).

-1, 4, 2, 10, 14, 34, 62, 130, 254, 514, 1022, 2050, 4094, 8194, 16382, 32770, 65534, 131074, 262142, 524290, 1048574, 2097154, 4194302, 8388610, 16777214, 33554434, 67108862, 134217730, 268435454, 536870914, 1073741822, 2147483650, 4294967294, 8589934594, 17179869182, 34359738370

Offset: 0

Author

Paul Curtz, Feb 18 2008

Keywords

• sign
• easy

Comments

First differences of A014551. - Reinhard Zumkeller, Jan 02 2013

It can be noticed that, once deprived of its first term, this is an "autosequence" of the second kind, whose companion of the first kind is A014113. - Jean-François Alcover, Aug 19 2022

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• OEIS Wiki, Autosequence
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Programs

Haskell

a135440 n = a135440_list !! n
a135440_list = zipWith (-) (tail a014551_list) a014551_list
-- Reinhard Zumkeller, Jan 02 2013

Mathematica

f[n_]:=2/(n+1);x=4;Table[x=f[x];Numerator[x],{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *)
LinearRecurrence[{1,2}, {-1,4}, 25] (* or *) Table[2^n - 2*(-1)^n, {n,0,25}] (* G. C. Greubel, Oct 14 2016 *)

Formula

From R. J. Mathar, Feb 19 2008: (Start)

O.g.f.: -1/(2*x-1) - 2/(1+x).

a(n) = 2^n - 2*(-1)^n. (End)

a(n) = 2*A014551(n-1), n>0. - Paul Curtz, Jun 01 2011

E.g.f.: exp(2*x) - 2*exp(-x). - G. C. Greubel, Oct 14 2016

Extensions

More terms from R. J. Mathar, Feb 19 2008