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%I #25 Mar 15 2024 14:22:10
%S 1,-3,8,-17,36,-71,140,-269,516,-979,1852,-3481,6516,-12127,22444,
%T -41253,75236,-135915,242716,-427185,737876,-1242743,2019468,-3106877,
%U 4349636,-4971011,2485500,9942071,-49710284,159072881,-437450388,1113510059,-2704238684,6362914533,-14634703396
%N Expansion of g.f. (1+x-2*x^2+x^3+x^4)/((1-x)^2*(1+x)^2*(1+2*x)^2).
%C Floretion Algebra Multiplication Program, FAMP Code: 2jbasekrokseq[ - .25'i - .25i' + 'ii' + .25'jk' + .25'kj'], RokType: Y[sqa.Findk()] = Y[sqa.Findk()] - p (internal program code)
%H G. C. Greubel, <a href="/A106691/b106691.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-2,8,7,-4,-4).
%F From _G. C. Greubel_, Sep 09 2021: (Start)
%F a(n) = (1/54)*(3*n +4 -27*(-1)^n*(n+4) +(-2)^(n+1)*(3*n-79)).
%F E.g.f.: (1/54)*((4 +3*x)*exp(x) -27*(4 -x)*exp(-x) + 2*(79 +6*x)*exp(-2*x)). (End)
%t CoefficientList[Series[(1+x-2x^2+x^3+x^4)/((1-x)^2(1+x)^2(1+2x)^2),{x,0,40}],x] (* or *) LinearRecurrence[{-4,-2,8,7,-4,-4},{1,-3,8,-17,36,-71},40] (* _Harvey P. Dale_, Dec 21 2015 *)
%o (Magma) [(1/54)*(3*n +4 -27*(-1)^n*(n+4) +(-2)^(n+1)*(3*n-79)): n in [0..40]]; // _G. C. Greubel_, Sep 09 2021
%o (SageMath) [(1/54)*(3*n +4 -27*(-1)^n*(n+4) +(-2)^(n+1)*(3*n-79)) for n in (0..40)] # _G. C. Greubel_, Sep 09 2021
%Y Cf. A002697.
%K sign,easy
%O 0,2
%A _Creighton Dement_, May 13 2005
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