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%I #14 May 14 2022 13:22:08
%S 1,0,2,5,5,4,13,29,34,39,89,176,233,313,610,1115,1597,2328,4181,7277,
%T 10946,16687,28657,48416,75025,117297,196418,326003,514229,815656,
%U 1346269,2211077,3524578,5637351,9227465
%N Expansion of -(1-x+3*x^2+x^3) / ((x^2+x-1)*(2*x^2+1)).
%C a(2n) = F(2n+1) = A001519(n).
%H Colin Barker, <a href="/A116698/b116698.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,2,2).
%F a(n) = a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) for n > 3. - _Colin Barker_, May 18 2019
%t CoefficientList[Series[-(1-x+3x^2+x^3)/((x^2+x-1)(2x^2+1)),{x,0,100}],x] (* or *) LinearRecurrence[{1,-1,2,2},{1,0,2,5},100] (* _Harvey P. Dale_, May 14 2022 *)
%o (PARI) Vec((1 - x + 3*x^2 + x^3) / ((1 - x - x^2)*(1 + 2*x^2)) + O(x^40)) \\ _Colin Barker_, May 18 2019
%Y Cf. A001519, A006498, A115008, A116697, A116699.
%K easy,nonn
%O 0,3
%A _Creighton Dement_, Feb 23 2006
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