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%I #15 Sep 08 2022 08:44:44
%S 1,25,439,6685,94471,1276405,16745119,215226205,2725568791,
%T 34135388485,423910350799,5229781276525,64185946519111,
%U 784517071831765,9557062002788479,116113315455883645,1407645499737869431
%N Expansion of 1/((1-3x)(1-10x)(1-12x)).
%H Vincenzo Librandi, <a href="/A018207/b018207.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 (25,-186,360).
%F a(0)=1, a(1)=25, a(2)=439; for n>2. a(n) = 25*a(n-1) -186*a(n-2) +360*a(n-3). - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = 22*a(n-1) -120*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = (7*12^(n+2) - 9*10^(n+2) + 2*3^(n+2))/126. [_Yahia Kahloune_, Jul 06 2013]
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)
%t LinearRecurrence[{25,-186,360},{1,25,439},20] (* _Harvey P. Dale_, Jul 20 2022 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-10*x)*(1-12*x)))); /* or */ I:=[1, 25, 439]; [n le 3 select I[n] else 25*Self(n-1)-186*Self(n-2)+360*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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