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Expansion of 1/((1-7*x)*(1-9*x)*(1-12*x)).
1

%I #31 Sep 08 2022 08:44:45

%S 1,28,529,8428,122257,1673980,22067473,283450636,3574941073,

%T 44501447452,548719235857,6718924954924,81849587868049,

%U 993294339107644,12020103854584081,145151139884150092,1750035954202640785

%N Expansion of 1/((1-7*x)*(1-9*x)*(1-12*x)).

%H G. C. Greubel, <a href="/A020972/b020972.txt">Table of n, a(n) for n = 0..923</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (28,-255,756).

%F a(n) = 28*a(n-1) - 255*a(n-2) + 756*a(n-3), n>=3. - _Vincenzo Librandi_, Mar 15 2011

%F a(n) = 21*a(n-1) - 108*a(n-2) + 7^n, a(0)=1, a(1)=28. - _Vincenzo Librandi_, Mar 15 2011

%F a(n) = (2*12^(n+2) - 5*9^(n+2) + 3*7^(n+2))/30. - _Yahia Kahloune_, Jun 30 2013

%t CoefficientList[Series[1/((1-7x)(1-9x)(1-12x)), {x,0,50}], x] (* _G. C. Greubel_, May 31 2018 *)

%t LinearRecurrence[{28,-255,756},{1,28,529},20] (* _Harvey P. Dale_, Oct 08 2020 *)

%o (PARI) x='x+O('x^50); Vec(1/((1-7*x)*(1-9*x)*(1-12*x))) \\ _G. C. Greubel_, May 31 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-7*x)*(1-9*x)*(1-12*x)))); // _G. C. Greubel_, May 31 2018

%K nonn

%O 0,2

%A _N. J. A. Sloane_