This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016765 #31 Mar 26 2025 17:23:58
%S A016765 1,13,115,865,5971,39193,249355,1555105,9573091,58428073,354585595,
%T A016765 2143759345,12928070611,77832076153,468051849835,2812563019585,
%U A016765 16892428846531,101422905135433,608811146458075,3653962903591825,21928165007708851,131586550851237913,789589579708426315
%N A016765 Expansion of g.f. 1/((1-3*x)*(1-4*x)*(1-6*x)).
%H A016765 G. C. Greubel, <a href="/A016765/b016765.txt">Table of n, a(n) for n = 0..1000</a>
%H A016765 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-54,72).
%F A016765 From _Vincenzo Librandi_, Mar 20 2011: (Start)
%F A016765 a(n) = 6^(n+1) - 2^(2*n+3) + 3^(n+1).
%F A016765 a(n) = 10*a(n-1) - 24*a(n-2) + 3^n, n >= 2. (End)
%F A016765 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
%F A016765 From _Elmo R. Oliveira_, Mar 26 2025: (Start)
%F A016765 E.g.f.: exp(3*x)*(6*exp(3*x) - 8*exp(x) + 3).
%F A016765 a(n) = 13*a(n-1) - 54*a(n-2) + 72*a(n-3).
%F A016765 a(n) = A016149(n+1) - A016137(n+1). (End)
%p A016765 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 A016765 Table[6^(n + 1) - 2^(2*n + 3) + 3^(n + 1), {n, 0, 20}] (* _Wesley Ivan Hurt_, May 15 2014 *)
%t A016765 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 A016765 (Magma) [6^(n+1)-2^(2*n+3)+3^(n+1): n in [0..20]]; // _Wesley Ivan Hurt_, May 15 2014
%o A016765 (PARI) vector(30,n,n--; 6^(n+1)-2^(2*n+3)+3^(n+1)) \\ _G. C. Greubel_, Sep 15 2018
%Y A016765 Cf. A016137, A016149.
%K A016765 nonn,easy
%O A016765 0,2
%A A016765 _N. J. A. Sloane_, Dec 11 1999