The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A128130 Expansion of (1-x)/(1+x^4); period 8: repeat [1,-1,0,0,-1,1,0,0]. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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). 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). a(n) = (1/8)*(-(n mod 8) + ((n+2) mod 8) - 2*((n+3) mod 8) + ((n+4) mod 8) - ((n+6) mod 8) + 2*((n+7) mod 8)), with n>=0. - Paolo P. Lava, Oct 23 2007 abs(a(n)) = A133872(n). - Wesley Ivan Hurt, Feb 23 2015 a(n) = A014017(n) - A014017(n-1). - R. J. Mathar, Feb 24 2015 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 *) PROG (Scheme) (define (A128130 n) (list-ref '(1 -1 0 0 -1 1 0 0) (modulo n 8))) ;; Antti Karttunen, Aug 12 2017 CROSSREFS Cf. A014017, A133872. Sequence in context: A073784 A320006 A219977 * A133872 A286903 A339052 Adjacent sequences:  A128127 A128128 A128129 * A128131 A128132 A128133 KEYWORD easy,sign AUTHOR Paul Barry, Feb 15 2007 EXTENSIONS More terms from Antti Karttunen, Aug 12 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)