A165326 a(0)=a(1)=1, a(n) = -a(n-1) for n > 1.

1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1

Offset: 0

Author

Philippe Deléham, Sep 14 2009

Keywords

• easy
• sign
• mult

Comments

Inverse binomial transform of A040000(n) = 1,2,2,2,2,...; binomial transform of (-1)^(n+1)*A000918(n) = 1,0,-2,6,-14,30,-62,... - Philippe Deléham, Sep 16 2009

This is also the Z-sequence of the Riordan triangle A105809. See the W. Lang link under A006232 for Riordan A- and Z-sequences. - Wolfdieter Lang, Oct 04 2014

Links

• Index entries for linear recurrences with constant coefficients, signature (-1).

Crossrefs

Cf. A033999.

Programs

Mathematica

PadRight[{1},120,{-1,1}] (* Harvey P. Dale, Dec 04 2012 *)
Join[{1},LinearRecurrence[{-1},{1},83]] (* Ray Chandler, Aug 12 2015 *)

Formula

G.f.: (1+2*x)/(1+x).

E.g.f.: 2-exp(-x).

a(n) = -a(n-1). - Wesley Ivan Hurt, Apr 23 2021