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%I #10 Mar 13 2024 19:26:21
%S 1,1,1,1,1,5,13,33,85,225,589,1541,4033,10561,27649,72385,189505,
%T 496133,1298893,3400545,8902741,23307681,61020301,159753221,418239361,
%U 1094964865,2866655233,7505000833,19648347265,51440040965,134671775629
%N Expansion of -(x+2*x^2+3*x^3-1+5*x^4)/((x+1)*(x^2-3*x+1)*(1+x^2)).
%C Floretion Algebra Multiplication Program, FAMP Code: 4jbaseksumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], sumtype: Y[15],inty[ * ]
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,1,2,-1).
%F a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(n)=2*a(n-1)+a(n-2)+a(n-3)+ 2*a(n-4)- a(n-5). - _Harvey P. Dale_, Apr 14 2015
%t CoefficientList[Series[-(x+2x^2+3x^3-1+5x^4)/((x+1)(x^2-3x+1)(1+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{2,1,1,2,-1},{1,1,1,1,1},40] (* _Harvey P. Dale_, Apr 14 2015 *)
%Y Cf. A111665, A111666.
%K easy,nonn
%O 0,6
%A _Creighton Dement_, Aug 14 2005
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