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Expansion of 1/((1-x)*(1-8*x)*(1-9*x)).
8

%I #27 Apr 20 2023 17:44:21

%S 1,18,235,2700,28981,298278,2984095,29253600,282456361,2695498938,

%T 25486623955,239196683700,2231306698141,20710052641998,

%U 191416812647815,1762962024789000,16188343910770321,148268580698287458,1355005110295423675,12359749064745505500

%N Expansion of 1/((1-x)*(1-8*x)*(1-9*x)).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-89,72)

%F G.f.: 1/((1-x)*(1-8*x)*(1-9*x)).

%F a(n) = 17*a(n-1) - 72*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011

%F a(n) = 9^(n+2)/8 - 8^(n+2)/7 + 1/56. - _R. J. Mathar_, Mar 14 2011

%F a(n) = 18*a(n-1) - 89*a(n-2) + 72*a(n-3). - _Wesley Ivan Hurt_, Apr 20 2023

%p a:=n->sum(9^(n-j)-8^(n-j),j=0..n): seq(a(n), n=1..19); # _Zerinvary Lajos_, Jan 04 2007

%t Table[(-8^(n + 2) + 7*9^(n + 1) + 1)/56, {n, 40}] (* and *) CoefficientList[Series[1/((1 - z) (1 - 8*z) (1 - 9*z)), {z, 0, 40}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *)

%o (PARI) Vec(1/((1-x)*(1-8*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 23 2012

%Y Cf. A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_