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%I #21 Mar 08 2024 12:13:57
%S 1,1,0,-1,0,3,4,-1,-8,-5,12,23,0,-45,-44,47,136,43,-228,-313,144,771,
%T 484,-1057,-2024,91,4140,3959,-4320,-12237,-3596,20879,28072,-13685,
%U -69828,-42457,97200,182115,-12284,-376513,-351944,401083,1104972,302807,-1907136,-2512749,1301524,6327023,3723976
%N a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 1, a(2) = 0.
%C Floretion Algebra Multiplication Program, FAMP Code: ibaseiseq[.5'j + .5'k + .5j' + .5k' + .5'ii' + .5e]
%H Colin Barker, <a href="/A105578/b105578.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,-3,2).
%F a(n) - a(n+1) = A001607(n); a(n+2) - 2a(n+1) + a(n) = - A078020(n).
%F G.f.: -(x^2-x+1) / ((x-1)*(2*x^2-x+1)). - _Colin Barker_, Feb 08 2015
%t -Join[{-1,-1,a=0,b=1},Table[c=1*b-2*a-1;a=b;b=c,{n,100}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 21 2011 *)
%t LinearRecurrence[{2,-3,2},{1,1,0},50] (* _Harvey P. Dale_, Mar 28 2019 *)
%o (PARI) Vec(-(x^2-x+1)/((x-1)*(2*x^2-x+1)) + O(x^100)) \\ _Colin Barker_, Feb 08 2015
%Y Cf. A002249, A014551, A078020, A105577, A105579.
%Y Equals (A107920(n) + 1)/2.
%K sign,easy
%O 0,6
%A _Creighton Dement_, Apr 14 2005
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