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

%I A016633 #29 Mar 26 2025 17:23:12
%S A016633 1,25,447,6989,101759,1417941,19180519,253983853,3309800367,
%T A016633 42599540357,542895780791,6863463633117,86197420501375,
%U A016633 1076563471968373,13382900349107463,165700329729679181,2044564737700501583,25152545442794015589,308625999807796411735,3778261997130507936445
%N A016633 Expansion of g.f. 1/((1-2*x)*(1-11*x)*(1-12*x)).
%H A016633 Vincenzo Librandi, <a href="/A016633/b016633.txt">Table of n, a(n) for n = 0..900</a>
%H A016633 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (25,-178,264).
%F A016633 From _Vincenzo Librandi_, Oct 09 2011: (Start)
%F A016633 a(n) = (648*12^n + 2^(n+1) - 5*11^(n+2))/45.
%F A016633 a(n) = 23*a(n-1) - 132*a(n-2) + 2^n.
%F A016633 a(n) = 25*a(n-1) - 178*a(n-2) + 264*a(n-3), n >= 3. (End)
%F A016633 From _Elmo R. Oliveira_, Mar 26 2025: (Start)
%F A016633 E.g.f.: exp(2*x)*(648*exp(10*x) - 605*exp(9*x) + 2)/45.
%F A016633 a(n) = A016136(n+1) - A016135(n+1). (End)
%t A016633 CoefficientList[Series[1/((1 - 2 x) (1 - 11 x) (1 - 12 x)), {x, 0, 15}], x] (* _Michael De Vlieger_, Jan 31 2018 *)
%o A016633 (Sage) [(12^n - 2^n)/10-(11^n - 2^n)/9 for n in range(2,18)] # _Zerinvary Lajos_, Jun 05 2009
%o A016633 (Magma) [(648*12^n +2^(n+1)-5*11^(n+2))/45 : n in [0..20]]; // _Vincenzo Librandi_, Oct 09 2011
%o A016633 (PARI) Vec(1/((1-2*x)*(1-11*x)*(1-12*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A016633 Cf. A006516, A016127, A016129, A016130, A016311, A016316, A016321, A016325. - _Zerinvary Lajos_, Jun 05 2009
%Y A016633 Cf. A016135, A016136.
%K A016633 nonn,easy
%O A016633 0,2
%A A016633 _N. J. A. Sloane_