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 A092202 Expansion of (x - x^3) / (1 - x^5) in powers of x. 3
 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Partial sums of A080891. LINKS M. E. Muldoon and A. A. Ungar, Beyond Sin and Cos, Mathematics Magazine, 69,1,(1996). Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1). FORMULA E.g.f. : F(1, 5, 1, x)-F(1, 5, 3, x); a(n) = Sum{k=0..n} Jacobi(k, 5). Euler transform of length 5 sequence [ 0, -1, 0, 0, 1]. - Michael Somos, Mar 26 2012 G.f.: (x + x^2) / (1 + x + x^2 + x^3 + x^4). a(n) = a(n + 5). a(-1 - n) = -a(n). a(5*n) = a(5*n + 2) = a(5*n+4) = 0. a(5*n + 1) = 1. a(5*n + 3) = -1. - Michael Somos, Mar 26 2012 EXAMPLE x - x^3 + x^6 - x^8 + x^11 - x^13 + x^16 - x^18 + x^21 - x^23 + x^26 + ... PROG (PARI) {a(n) = (n%5 == 1) - (n%5 == 3)} /* Michael Somos, Mar 26 2012 */ CROSSREFS Cf. A080891. Sequence in context: A241422 A189661 A145573 * A285686 A303591 A159684 Adjacent sequences:  A092199 A092200 A092201 * A092203 A092204 A092205 KEYWORD easy,sign AUTHOR Paul Barry, Feb 24 2004 STATUS approved

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Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)