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%I #14 Sep 08 2022 08:44:44
%S 1,24,397,5628,73513,914112,11008549,129690276,1504024705,17241418920,
%T 195930981181,2211723344844,24837316537177,277785786712848,
%U 3096821665511893,34435641499407732,382127489397444529,4233421296687394296,46837804552120354285
%N Expansion of 1/((1-4x)(1-9x)(1-11x)).
%H Vincenzo Librandi, <a href="/A019687/b019687.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,-179,396).
%F a(n) = 4^(n+2)/35 +11^(n+2)/14 -9^(n+2)/10. - _R. J. Mathar_, Nov 11 2012
%F a(0)=1, a(1)=24, a(2)=397; for n>2, a(n) = 24*a(n-1) -179*a(n-2) +396*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 20*a(n-1) -99*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%p a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [24, -179, 396][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{24,-179,396},{1,24,397},20] (* _Harvey P. Dale_, Nov 16 2021 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-9*x)*(1-11*x)))); /* or */ I:=[1, 24, 397]; [n le 3 select I[n] else 24*Self(n-1)-179*Self(n-2)+396*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.