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%I #16 Sep 08 2022 08:44:45
%S 1,24,393,5480,70161,853944,10066393,116192520,1322205921,14898923864,
%T 166735197993,1856912289960,20608880226481,228161663489784,
%U 2521496249891193,27830232878409800,306882907287251841
%N Expansion of 1/((1-5x)(1-8x)(1-11x)).
%H Vincenzo Librandi, <a href="/A020447/b020447.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 (24,-183,440).
%F a(n) = 25*5^n/18 -64*8^n/9 +121*11^n/18. - _R. J. Mathar_, Jun 29 2013
%F a(0)=1, a(1)=24, a(2)=393; for n>2, a(n) = 24*a(n-1) -183*a(n-2) +440*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 19*a(n-1) -88*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{24,-183,440},{1,24,393},30] (* _Harvey P. Dale_, Jun 20 2015 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-11*x)))); /* or */ I:=[1, 24, 393]; [n le 3 select I[n] else 24*Self(n-1)-183*Self(n-2)+440*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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