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%I #17 Oct 01 2016 05:48:45
%S 30,42,146,346,942,2430,6398,16714,43794,114618,300110,785662,2056926,
%T 5385066,14098322,36909850,96631278,252983934,662320574,1733977738,
%U 4539612690,11884860282,31114968206,81460044286,213265164702,558335449770,1461741184658,3826888104154
%N Expansion of 2*(x^2-9*x+15) / ((1+x)*(1-3*x+x^2)).
%H Colin Barker, <a href="/A090692/b090692.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1).
%F a(0)=30, a(1)=42, a(2)=146, a(n) = 2*a(n-1)+2*a(n-2)-a(n-3). - _Harvey P. Dale_, Aug 21 2014
%F a(n) = (2^(1-n)*(25*(-2)^n+(25-11*sqrt(5))*(3-sqrt(5))^n+(3+sqrt(5))^n*(25+11*sqrt(5))))/5. - _Colin Barker_, Oct 01 2016
%t CoefficientList[Series[2(x^2-9x+15)/(x^3-2x^2-2x+1),{x,0,30}],x] (* or *) LinearRecurrence[{2,2,-1},{30,42,146},30] (* _Harvey P. Dale_, Aug 21 2014 *)
%o (PARI) a(n) = round((2^(1-n)*(25*(-2)^n+(25-11*sqrt(5))*(3-sqrt(5))^n+(3+sqrt(5))^n*(25+11*sqrt(5))))/5) \\ _Colin Barker_, Oct 01 2016
%o (PARI) Vec(2*(x^2-9*x+15)/((1+x)*(1-3*x+x^2)) + O(x^40)) \\ _Colin Barker_, Oct 01 2016
%K nonn,easy
%O 0,1
%A _Creighton Dement_, Jan 08 2005
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