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%I #23 Sep 08 2022 08:45:28
%S 1,3,9,31,109,391,1397,4995,17833,63675,227313,811543,2897269,
%T 10343647,36928061,131837979,470678161,1680380979,5999172633,
%U 21417807055,76464283837,272987183095,974598829637,3479441311347,12422046335161
%N Expansion of -x * (x-1) * (3*x^2-1) / (9*x^4-8*x^3+4*x-1).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-8,9).
%F From _Colin Barker_, Oct 19 2012: (Start)
%F a(n) = 4*a(n-1) -8*a(n-3) +9*a(n-4).
%F G.f.: -x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1). (End)
%p seq(coeff(series(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1),x,n+1), x, n), n = 1 .. 25); # _Muniru A Asiru_, Oct 13 2018
%t LinearRecurrence[{4,0,-8,9},{1,3,9,31},30] (* _Harvey P. Dale_, Jul 26 2018 *)
%o (PARI) x='x+O('x^30); Vec(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1)) \\ _G. C. Greubel_, Oct 12 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(-x*(x-1)*(3*x^2-1)/(9*x^4-8*x^3+4*x-1))); // _G. C. Greubel_, Oct 12 2018
%Y Cf. A000952, A074872, A085340, A003432.
%K nonn,less
%O 1,2
%A _Roger L. Bagula_, Oct 05 2006
%E Sequence edited by _Joerg Arndt_ and _Colin Barker_, Oct 19 2012
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