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A092202 Expansion of (x - x^3) / (1 - x^5) in powers of x. 3

%I

%S 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,

%T 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,

%U 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

%N Expansion of (x - x^3) / (1 - x^5) in powers of x.

%C Partial sums of A080891.

%H M. E. Muldoon and A. A. Ungar, <a href="http://www.jstor.org/stable/2691389">Beyond Sin and Cos</a>, Mathematics Magazine, 69,1,(1996).

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

%F E.g.f. : F(1, 5, 1, x)-F(1, 5, 3, x);

%F a(n) = Sum{k=0..n} Jacobi(k, 5).

%F Euler transform of length 5 sequence [ 0, -1, 0, 0, 1]. - _Michael Somos_, Mar 26 2012

%F G.f.: (x + x^2) / (1 + x + x^2 + x^3 + x^4).

%F 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

%e x - x^3 + x^6 - x^8 + x^11 - x^13 + x^16 - x^18 + x^21 - x^23 + x^26 + ...

%o (PARI) {a(n) = (n%5 == 1) - (n%5 == 3)} /* _Michael Somos_, Mar 26 2012 */

%Y Cf. A080891.

%K easy,sign

%O 0,1

%A _Paul Barry_, Feb 24 2004

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Last modified June 2 11:20 EDT 2020. Contains 334771 sequences. (Running on oeis4.)