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%I #14 Jul 28 2022 09:05:37
%S 0,1,4,10,21,40,71,121,204,348,609,1097,2021,3767,7035,13082,24160,
%T 44318,80883,147201,267702,487225,888115,1621465,2964090,5422351,
%U 9921404,18150445,33193146,60679800,110893986,202625306,370215059,676438568,1236053904
%N Expansion of x/(1 - 4*x + 6*x^2 - 5*x^3 + 4*x^4 - 3*x^5).
%H Vincenzo Librandi, <a href="/A144897/b144897.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-4,3).
%F G.f.: x/(1 - 4*x + 6*x^2 - 5*x^3 + 4*x^4 - 3*x^5).
%p a:= n-> (Matrix(5, (i,j)-> if i=j-1 then 1 elif j=1 then [4, -6, 5, -4, 3, -1][i] else 0 fi)^n)[1,2]: seq(a(n), n=0..40);
%t CoefficientList[Series[x/(1 -4x +6x^2 -5x^3 +4x^4 -3x^5), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x/(1-4*x+6*x^2-5*x^3+4*x^4-3*x^5) )); // _G. C. Greubel_, Jul 27 2022
%o (Sage)
%o def A144897_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( x/(1-4*x+6*x^2-5*x^3+4*x^4-3*x^5) ).list()
%o A144897_list(50) # _G. C. Greubel_, Jul 27 2022
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 24 2008
%E Definition corrected at the suggestion of _Vincenzo Librandi_ by _Alois P. Heinz_, Jun 06 2013
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