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Expansion of 1/((1-7*x)*(1-9*x)*(1-11*x)).
1

%I #42 Sep 08 2022 08:44:45

%S 1,27,490,7470,103291,1343097,16753780,202932540,2405791381,

%T 28065859767,323426323870,3691983687210,41834308968271,

%U 471276683342037,5284615302054760,59040661951743480,657669557062017961

%N Expansion of 1/((1-7*x)*(1-9*x)*(1-11*x)).

%H G. C. Greubel, <a href="/A020971/b020971.txt">Table of n, a(n) for n = 0..957</a> (terms 0..133 from Charles R Greathouse IV)

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27,-239,693).

%F a(n) = 27*a(n-1) - 239*a(n-2) + 693*a(n-3), n>=3. - _Vincenzo Librandi_, Mar 15 2011

%F a(n) = 20*a(n-1) - 99*a(n-2) + 7^n, a(0)=1, a(1)=27. - _Vincenzo Librandi_, Mar 15 2011

%F a(n) = (7^(n+2)-2*9^(n+2)+11^(n+2))/8. - _Bruno Berselli_, Mar 15 2011

%t CoefficientList[Series[1/((1-7x)(1-9x)(1-11x)),{x,0,20}],x] (* or *) LinearRecurrence[{27,-239,693},{1,27,490},20] (* _Harvey P. Dale_, Oct 31 2017 *)

%o (PARI) Vec(1/((1-7*x)*(1-9*x)*(1-11*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (PARI) a(n)=n+=2;(7^n-2*9^n+11^n)/8 \\ _Charles R Greathouse IV_, Apr 01 2016

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-7*x)*(1-9*x)*(1-11*x)))); // _G. C. Greubel_, May 31 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_