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 A083882 #19 May 07 2025 09:13:10
%S A083882 1,4,19,100,553,3124,17803,101812,583057,3340900,19147459,109747972,
%T A083882 629066809,3605810836,20668618171,118473404500,679095199777,
%U A083882 3892607339716,22312621120627,127897073548708,733112513821513
%N A083882 a(0)=1, a(1)=4, a(n)=8a(n-1)-13a(n-2), n>=2.
%C A083882 Binomial transform of A083881.
%H A083882 Michael De Vlieger, <a href="/A083882/b083882.txt">Table of n, a(n) for n = 0..1319</a>
%H A083882 Yassine Otmani, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Otmani/otmani10.html">The 2-Pascal Triangle and a Related Riordan Array</a>, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 12.
%H A083882 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13).
%F A083882 a(n) = ((4-sqrt(3))^n+(4+sqrt(3))^n)/2.
%F A083882 a(n) = Sum_{k=0..floor(n/2)} C(n, 2k)4^(n-2k)3^k.
%F A083882 G.f.: (1-4x)/(1-8x+13x^2);
%F A083882 E.g.f.: exp(4x)cosh(x*sqrt(3)).
%F A083882 a(n) = Sum_{k=0..n} A027907(n,2k)*3^k . - _J. Conrad_, Aug 24 2016
%t A083882 LinearRecurrence[{8,-13},{1,4},30] (* _Harvey P. Dale_, Aug 02 2015 *)
%K A083882 easy,nonn
%O A083882 0,2
%A A083882 _Paul Barry_, May 08 2003