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A018912 Expansion of 1/((1-4x)(1-5x)(1-10x)). 2

%I

%S 1,19,251,2879,30891,320439,3266131,32986399,331554971,3324266759,

%T 33287301411,333100377519,3332157369451,33327408774679,

%U 333303531583091,3333183608754239,33332581847126331,333329564449052199

%N Expansion of 1/((1-4x)(1-5x)(1-10x)).

%H Vincenzo Librandi, <a href="/A018912/b018912.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 (19,-110,200).

%F a(n) = 8*4^n/3 -5*5^n/1 +10*10^n/3. - _R. J. Mathar_, Jun 29 2013

%F a(0)=1, a(1)=19, a(2)=251; for n>2, a(n) = 19*a(n-1) -110*a(n-2) +200*a(n-3). - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = 15*a(n-1) -50*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 02 2013

%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 5 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2012 *)

%o (MAGMA) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-10*x)))); /* or */ I:=[1, 19, 251]; [n le 3 select I[n] else 19*Self(n-1)-110*Self(n-2)+200*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)