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%I #21 Nov 11 2024 03:47:33
%S 1,15,171,1755,17091,161595,1501011,13789035,125780931,1142106075,
%T 10339420851,93417584715,842935044771,7599476096955,68473649036691,
%U 616733026314795,5553418346740611,49997691780110235
%N Expansion of 1/((1-6*x)*(1-9*x)).
%H G. C. Greubel, <a href="/A016172/b016172.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (15,-54).
%F a(n) = (9^(n+1) - 6^(n+1))/3. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
%F a(0)=1, a(n) = 9*a(n-1) + 6^n. - _Vincenzo Librandi_, Feb 09 2011
%F a(0)=1, a(1)=15, a(n) = 15*a(n-1) - 54*a(n-2). - _Vincenzo Librandi_, Feb 09 2011
%F E.g.f.: 3*exp(9*x) - 2*exp(6*x). - _G. C. Greubel_, Nov 10 2024
%t Table[(9^(n+1)-6^(n+1))/3, {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t CoefficientList[Series[1/((1-6x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[{15,-54},{1,15},30] (* _Harvey P. Dale_, Oct 07 2015 *)
%o (PARI) Vec(1/((1-6*x)*(1-9*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) [n le 2 select 15^(n-1) else 15*Self(n-1) -54*Self(n-2): n in [1..31]]; // _G. C. Greubel_, Nov 10 2024
%o (SageMath)
%o A016172=BinaryRecurrenceSequence(15,-54,1,15)
%o [A016172(n) for n in range(31)] # _G. C. Greubel_, Nov 10 2024
%Y Cf. A016129.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_