%I #25 Sep 08 2022 08:44:41
%S 1,13,115,865,5971,39193,249355,1555105,9573091,58428073,354585595,
%T 2143759345,12928070611,77832076153,468051849835,2812563019585,
%U 16892428846531,101422905135433,608811146458075,3653962903591825,21928165007708851,131586550851237913
%N Expansion of 1/((1-3*x)*(1-4*x)*(1-6*x)).
%H G. C. Greubel, <a href="/A016765/b016765.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-54,72).
%F a(n) = 6^(n+1) - 2^(2*n+3) + 3^(n+1). - _Vincenzo Librandi_, Mar 20 2011
%F a(n) = 10*a(n-1) - 24*a(n-2) + 3^n, n >= 2. - _Vincenzo Librandi_, Mar 20 2011
%F G.f.: 1/((1-3*x)*(1-4*x)*(1-6*x)) = -3/(1-3*x) + 8/(1-4*x) - 6/(1-6*x). - _Wolfdieter Lang_, May 19 2014
%p A016765:=n->6^(n+1)-2^(2*n+3)+3^(n+1); seq(A016765(n), n=0..20); # _Wesley Ivan Hurt_, May 15 2014
%t Table[6^(n + 1) - 2^(2*n + 3) + 3^(n + 1), {n, 0, 20}] (* _Wesley Ivan Hurt_, May 15 2014 *)
%t CoefficientList[Series[1/((1-3x)(1-4x)(1-6x)),{x,0,30}],x] (* or *) LinearRecurrence[{13,-54,72},{1,13,115},30] (* _Harvey P. Dale_, Jul 18 2021 *)
%o (Magma) [6^(n+1)-2^(2*n+3)+3^(n+1): n in [0..20]]; // _Wesley Ivan Hurt_, May 15 2014
%o (PARI) vector(30,n,n--; 6^(n+1)-2^(2*n+3)+3^(n+1)) \\ _G. C. Greubel_, Sep 15 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 11 1999