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%I #13 Sep 23 2021 14:09:15
%S 1,-2,-7,-7,2,13,13,-2,-19,-19,2,25,25,-2,-31,-31,2,37,37,-2,-43,-43,
%T 2,49,49,-2,-55,-55,2,61,61,-2,-67,-67,2,73,73,-2,-79,-79,2,85,85,-2,
%U -91,-91,2,97,97,-2,-103,-103,2,109,109,-2,-115,-115,2,121,121,-2
%N Expansion of (1-4x-x^3)/(1-x+x^2)^2.
%C Hankel transform of A079309.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-3,2,-1).
%F a(n) = (2n+1)*cos(Pi*n/3) - (2n+5)*sin(Pi*n/3)/sqrt(3).
%F a(n) = 2*a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) for n > 3. - _Jinyuan Wang_, Apr 09 2020
%t CoefficientList[Series[(1-4x-x^3)/(1-x+x^2)^2,{x,0,100}],x] (* or *) LinearRecurrence[{2,-3,2,-1},{1,-2,-7,-7},100] (* _Harvey P. Dale_, Sep 23 2021 *)
%o (PARI) Vec((1-4*x-x^3)/(1-x+x^2)^2 + O(x^62)) \\ _Jinyuan Wang_, Apr 09 2020
%Y Cf. A079309, A138342.
%K sign,easy
%O 0,2
%A _Paul Barry_, Mar 15 2008
%E More terms from _Jinyuan Wang_, Apr 09 2020