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%I #13 Sep 08 2022 08:44:44
%S 1,22,337,4450,54301,631462,7111417,78287530,847442101,9055541902,
%T 95785566097,1004927161810,10472915657101,108541954516342,
%U 1119734731454377,11506184005511290,117841370316867301
%N Expansion of 1/((1-3x)(1-9x)(1-10x)).
%H Vincenzo Librandi, <a href="/A018090/b018090.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 (22,-147,270).
%F a(0)=1, a(1)=22, a(2)=337; for n>2 a(n) = 22*a(n-1) -147*a(n-2) +270*a(n-3). - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = 19*a(n-1) -90*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = (6*10^(n+2) - 7*9^(n+2) + 3^(n+2))/42. [_Yahia Kahloune_, Jul 06 2013]
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-9*x)*(1-10*x)))); /* or */ I:=[1, 22, 337]; [n le 3 select I[n] else 22*Self(n-1)-147*Self(n-2)+270*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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