A143431 Periodic length 8 sequence [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, 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

Michael Somos, Aug 14 2008

Keywords

• sign
• easy

Comments

Nonsimple continued fraction expansion of (1+sqrt 5)/2= A001622. - R. J. Mathar, Mar 08 2012

Examples

			1 - x + x^2 - x^3 - x^4 + x^5 - x^6 + x^7 + x^8 - x^9 + x^10 - x^11 + ...
		

Crossrefs

Convolution inverse of A143432.

Programs

Mathematica

LinearRecurrence[{0,0,0,-1},{1,-1,1,-1},120] (* or *) PadRight[{},120,{1,-1,1,-1,-1,1,-1,1}] (* Harvey P. Dale, Jul 15 2025 *)

PARI

a(n) = (-1)^(n + n\4)

Formula

Euler transform of length 8 sequence [ -1, 1, 0, -2, 0, 0, 0, 1].

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

G.f.: (1 - x) * (1 + x^2) / (1 + x^4).