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A016633 Expansion of 1/((1-2x)(1-11x)(1-12x)). 1

%I

%S 1,25,447,6989,101759,1417941,19180519,253983853,3309800367,

%T 42599540357,542895780791,6863463633117,86197420501375,

%U 1076563471968373,13382900349107463,165700329729679181

%N Expansion of 1/((1-2x)(1-11x)(1-12x)).

%H Vincenzo Librandi, <a href="/A016633/b016633.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec&#34;order_03">Index entries for linear recurrences with constant coefficients</a>, signature (25,-178,264).

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

%F a(n) = (648*12^n + 2^(n+1) - 5*11^(n+2))/45.

%F a(n) = 23*a(n-1) - 132*a(n-2) + 2^n.

%F a(n) = 25*a(n-1) - 178*a(n-2) + 264*a(n-3), n >= 3. (End)

%t CoefficientList[Series[1/((1 - 2 x) (1 - 11 x) (1 - 12 x)), {x, 0, 15}], x] (* _Michael De Vlieger_, Jan 31 2018 *)

%o (Sage) [(12^n - 2^n)/10-(11^n - 2^n)/9 for n in xrange(2,18)] # _Zerinvary Lajos_, Jun 05 2009

%o (MAGMA) [(648*12^n +2^(n+1)-5*11^(n+2))/45 : n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011

%o (PARI) Vec(1/((1-2*x)*(1-11*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%Y Cf. A006516, A016127, A016129, A016130, A016311, A016316, A016321, A016325. - _Zerinvary Lajos_, Jun 05 2009

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified April 25 12:19 EDT 2019. Contains 322456 sequences. (Running on oeis4.)