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%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
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