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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Sequence in context: A075086 A284782 A128781 * A215500 A188128 A336914

Adjacent sequences: A135437 A135438 A135439 * A135441 A135442 A135443

Keyword

sign,easy

Author

Paul Curtz, Feb 18 2008

Extensions

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

Status

approved