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%I #15 Feb 27 2023 16:27:44
%S 1,25,426,6170,81851,1029315,12498676,148149460,1726010901,
%T 19855374605,226242178526,2559210312750,28786474721551,
%U 322368894171895,3597522989519976,40035969784960040,444564772324613801
%N Expansion of 1/((1-5x)(1-9x)(1-11x)).
%H Vincenzo Librandi, <a href="/A020499/b020499.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (25,-199,495).
%F a(n) = 25*5^n/24 -81*9^n/8 +121*11^n/12. - _R. J. Mathar_, Jun 30 2013
%F a(0)=1, a(1)=25, a(2)=426; for n>2, a(n) = 25*a(n-1) -199*a(n-2) +495*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 20*a(n-1) -99*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{25,-199,495},{1,25,426},20] (* _Harvey P. Dale_, Feb 27 2023 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 25, 426]; [n le 3 select I[n] else 25*Self(n-1)-199*Self(n-2)+495*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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