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A016321 Expansion of 1/((1-2x)(1-9x)(1-10x)). 6

%I

%S 1,21,313,4065,49081,566721,6350473,69654225,751887961,8016991521,

%T 84652923433,886876310385,9231886792441,95586981129921,

%U 985282830165193,10117545471478545,103557909243290521,1057021183189581921

%N Expansion of 1/((1-2x)(1-9x)(1-10x)).

%H Vincenzo Librandi, <a href="/A016321/b016321.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (21,-128,180).

%F From _Zerinvary Lajos_, Jun 05 2009 [corrected by _R. J. Mathar_, Mar 14 2011]: (Start)

%F a(n) = 2^(n-1)/7 - 9^(n+2)/7 + 25*10^n/2.

%F a(n) = A016134(n+1) - A016133(n+1). (End)

%F From _Vincenzo Librandi_, Oct 09 2011: (Start)

%F a(n) = (175*10^n + 2^n - 2*9^(n+2))/14.

%F a(n) = 19*a(n-1) - 90*a(n-2) + 2^n.

%F a(n) = 21*a(n-1) - 128*a(n-2) + 180*a(n-3), n >= 3. (End)

%t CoefficientList[Series[1/((1-2x)(1-9x)(1-10x)),{x,0,20}],x] (* or *) LinearRecurrence[{21,-128,180},{1,21,313},20] (* _Harvey P. Dale_, Aug 18 2014 *)

%o (Sage) [(10^n - 2^n)/8-(9^n - 2^n)/7 for n in xrange(2,20)] # _Zerinvary Lajos_, Jun 05 2009

%o (MAGMA) [(175*10^n +2^n-2*9^(n+2))/14 : n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011

%o (PARI) a(n) = (175*10^n+2^n-162*9^n)/14 \\ _Charles R Greathouse IV_, Sep 23 2012

%Y Cf. A016133, A016134.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified May 23 05:03 EDT 2019. Contains 323508 sequences. (Running on oeis4.)