A128130 - OEIS

%I #36 Dec 14 2023 05:27:44

%S 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,

%T 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,

%U -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

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

%H Antti Karttunen, <a href="/A128130/b128130.txt">Table of n, a(n) for n = 0..8191</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,-1).

%F 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).

%F abs(a(n)) = A133872(n). - _Wesley Ivan Hurt_, Feb 23 2015

%F a(n) = A014017(n) - A014017(n-1). - _R. J. Mathar_, Feb 24 2015

%p A128130 := proc(n)

%p     local m ;

%p     m := modp(n,8) ;

%p     op(1+m,[1,-1,0,0,-1,1,0,0]) ;

%p end proc: # _R. J. Mathar_, Feb 24 2015

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

%o (Scheme) (define (A128130 n) (list-ref '(1 -1 0 0 -1 1 0 0) (modulo n 8))) ;; _Antti Karttunen_, Aug 12 2017

%Y Cf. A014017, A133872.

%K easy,sign

%O 0,1

%A _Paul Barry_, Feb 15 2007

%E More terms from _Antti Karttunen_, Aug 12 2017