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%I #18 Sep 08 2022 08:44:40
%S 1,21,322,4362,55363,675423,8027524,93683604,1078947205,12304267305,
%T 139269572806,1567268992926,17557692150727,195994212714867,
%U 2181672731375368,24230027568735528,268614950968549129,2973526290066165309,32877645655436942410,363173810392188482610
%N Expansion of 1/((1-x)(1-9x)(1-11x)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-119,99).
%F a(n) = (4*11^(n+2)-5*9^(n+2)+1)/80. - _Bruno Berselli_, Mar 21 2011
%F a(n) = 20*a(n-1)-99*a(n-2)+1, n>=2. - _Vincenzo Librandi_, Mar 21 2011
%F a(n) = 21*a(n-1)-119*a(n-2)+99*a(n-3). - _Wesley Ivan Hurt_, Mar 27 2015
%p a:=n->sum((11^(n-j)-9^(n-j))/2,j=0..n): seq(a(n), n=1..17); # _Zerinvary Lajos_, Jan 12 2007
%t CoefficientList[Series[1/((1 - x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}],x] (* _Wesley Ivan Hurt_, Mar 27 2015 *)
%t LinearRecurrence[{21,-119,99},{1,21,322},20] (* _Harvey P. Dale_, Jun 07 2022 *)
%o (Magma) [(4*11^(n+2)-5*9^(n+2)+1)/80 : n in [0..20]]; // _Wesley Ivan Hurt_, Mar 27 2015
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_