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%I #11 May 03 2017 21:59:18
%S 0,1,1,3,1,2,3,5,2,3,5,7,3,4,7,9,4,5,9,11,5,6,11,13,6,7,13,15,7,8,15,
%T 17,8,9,17,19,9,10,19,21,10,11,21,23,11,12,23,25,12,13,25,27,13,14,27,
%U 29,14,15,29,31,15,16,31,33,16,17,33,35,17,18,35,37,18,19,37,39,19,20,39,41,20
%N Expansion of x*(1+3*x^2-2*x^3+2*x^4-x^5)/((1+x)*(x-1)^2*(x^2+1)^2).
%C The fractions A005563(n+1)/A000290(n+1) are 3, 8/4, 15/9, 24/16...,
%C in reduced form = 3, 2, 5/3, 3/2, 7/5... = a(2n+3)/a(2n+2).
%C The sequence shows the denominator-numerator pairs of the fractions.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 1, 1, -1, 1, -1).
%F G.f.: x*(1+3*x^2-2*x^3+2*x^4-x^5)/((1+x)*(x-1)^2*(x^2+1)^2).
%F a(n) = +a(n-1) -a(n-2) +a(n-3) +a(n-4) -a(n-5) +a(n-6) -a(n-7).
%F a(2n) = A026741(n). a(2n+1) = A026741(n+2).
%t CoefficientList[Series[x*(1 + 3*x^2 - 2*x^3 + 2*x^4 - x^5)/((1 + x)*(x - 1)^2*(x^2 + 1)^2), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, May 03 2017 *)
%Y Cf. A000290, A005563, A026741.
%K nonn,less
%O 0,4
%A _Paul Curtz_, Feb 13 2010
%E Edited by _R. J. Mathar_, Feb 24 2010