A128130 Expansion of (1-x)/(1+x^4); period 8: repeat [1,-1,0,0,-1,1,0,0].

1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0

Offset: 0

Author

Paul Barry, Feb 15 2007

Keywords

• easy
• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,-1).

Crossrefs

Cf. A014017, A133872.

Programs

Maple

A128130 := proc(n)
    local m ;
    m := modp(n,8) ;
    op(1+m,[1,-1,0,0,-1,1,0,0]) ;
end proc: # R. J. Mathar, Feb 24 2015

Mathematica

CoefficientList[Series[(1-x)/(1+x^4),{x,0,100}],x]  (* Harvey P. Dale, Mar 28 2011 *)

Scheme

(define (A128130 n) (list-ref '(1 -1 0 0 -1 1 0 0) (modulo n 8))) ;; Antti Karttunen, Aug 12 2017

Formula

a(n) = (sqrt(2)/4 + 1/2)*cos(3*Pi*n/4) - sqrt(2)*sin(3*Pi*n/4)/4 + (1/2 - sqrt(2)/4)*cos(Pi*n/4) - sqrt(2)*sin(Pi*n/4)/4; a(n) = Im(Sum_{k=0..n} i^(n-k+1)), i=sqrt(-1).

abs(a(n)) = A133872(n). - Wesley Ivan Hurt, Feb 23 2015

a(n) = A014017(n) - A014017(n-1). - R. J. Mathar, Feb 24 2015

Extensions

More terms from Antti Karttunen, Aug 12 2017