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Expansion of 1/((1-5x)(1-9x)(1-10x)).
1

%I #16 Sep 08 2022 08:44:45

%S 1,24,391,5394,67921,808164,9257851,103242534,1128792181,12157176504,

%T 129404822911,1364594578074,14281107062041,148528742855244,

%U 1536752582181571,15830742722056014,162476531910613501

%N Expansion of 1/((1-5x)(1-9x)(1-10x)).

%H Vincenzo Librandi, <a href="/A020494/b020494.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,-185,450).

%F a(n) = 5*5^n/4 -81*9^n/4 +20*10^n. - _R. J. Mathar_, Jun 30 2013

%F a(0)=1, a(1)=24, a(2)=391; for n>2, a(n) = 24*a(n-1) -185*a(n-2) +450*a(n-3). - _Vincenzo Librandi_, Jul 03 2013

%F a(n) = 19*a(n-1) -90*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013

%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)

%t LinearRecurrence[{24,-185,450},{1,24,391},20] (* _Harvey P. Dale_, Nov 27 2014 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-9*x)*(1-10*x)))); /* or */ I:=[1, 24, 391]; [n le 3 select I[n] else 24*Self(n-1)-185*Self(n-2)+450*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.