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 A081685 #20 Sep 05 2025 19:47:49
%S A081685 1,0,-2,24,382,3480,26398,183624,1217662,7844280,49595998,309603624,
%T A081685 1915345342,11771312280,71987479198,438579414024,2664184199422,
%U A081685 16146411375480,97676153291998,590010215086824,3559688013155902,21455704981601880,129219894496730398,777738831236334024
%N A081685 a(n) = 6^n - 5^n - 4^n - 3^n + 3*2^n.
%C A081685 Original name was: A sum of decreasing powers.
%H A081685 Zhuorui He, <a href="/A081685/b081685.txt">Table of n, a(n) for n = 0..1000</a>
%H A081685 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (20,-155,580,-1044,720).
%F A081685 a(n) = 6^n - 5^n - 4^n - 3^n + 3*2^n.
%F A081685 G.f.:(-1-636*x^4+516*x^3-153*x^2+20*x)/((6*x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
%F A081685 a(0)=1, a(1)=0, a(2)=-2, a(3)=24, a(4)=382, a(n) = 20*a(n-1) - 155*a(n-2) + 580*a(n-3) - 1044*a(n-4) + 720*a(n-5). - _Harvey P. Dale_, Sep 15 2014
%F A081685 E.g.f.: exp(2*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3). - _Elmo R. Oliveira_, Sep 12 2024
%t A081685 Table[6^n-5^n-4^n-3^n+3*2^n,{n,0,30}] (* or *) LinearRecurrence[{20,-155,580,-1044,720},{1,0,-2,24,382},30] (* _Harvey P. Dale_, Sep 15 2014 *)
%Y A081685 Binomial transform of A081684.
%K A081685 easy,sign,changed
%O A081685 0,3
%A A081685 _Paul Barry_, Mar 30 2003
%E A081685 a(23) from _Elmo R. Oliveira_, Sep 12 2024
%E A081685 New name from formula from _Zhuorui He_, Sep 05 2025