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 A190978 #32 Jul 06 2023 15:23:34
%S A190978 0,1,8,58,416,2980,21344,152872,1094912,7842064,56167040,402283936,
%T A190978 2881269248,20636450368,147803987456,1058613197440,7582081654784,
%U A190978 54304974053632,388947302500352,2785748575681024,19952304790446080,142903946869482496,1023517746213183488
%N A190978 a(n) = 8*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.
%H A190978 G. C. Greubel, <a href="/A190978/b190978.txt">Table of n, a(n) for n = 0..1000</a>
%H A190978 Pamela Fleischmann, Jonas Höfer, Annika Huch, and Dirk Nowotka, <a href="https://arxiv.org/abs/2306.14192">alpha-beta-Factorization and the Binary Case of Simon's Congruence</a>, arXiv:2306.14192 [math.CO], 2023.
%H A190978 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-6).
%F A190978 a(n) = ((4 + sqrt(10))^n - (4 - sqrt(10))^n)/(2*sqrt(10)). - _Giorgio Balzarotti_, May 28 2011
%F A190978 G.f.: x/(1 - 8*x + 6*x^2). - _Philippe Deléham_, Oct 12 2011
%F A190978 From _G. C. Greubel_, Jun 17 2022: (Start)
%F A190978 a(n) = 6^((n-1)/2)*ChebyshevU(n-1, 4/sqrt(6)).
%F A190978 E.g.f.: (1/sqrt(10))*exp(4*x)*sinh(sqrt(10)*x). (End)
%t A190978 LinearRecurrence[{8,-6}, {0,1}, 50]
%t A190978 CoefficientList[Series[x/(1-8x+6x^2),{x,0,30}],x] (* _Harvey P. Dale_, Aug 03 2021 *)
%o A190978 (Magma) [n le 2 select n-1 else 8*Self(n-1) -6*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Jun 17 2022
%o A190978 (SageMath) [sum( (-1)^k*binomial(n-k-1, k)*6^k*8^(n-2*k-1) for k in (0..((n-1)//2))) for n in (0..40)] # _G. C. Greubel_, Jun 17 2022
%Y A190978 Cf. A190958 (index to generalized Fibonacci sequences).
%K A190978 nonn
%O A190978 0,3
%A A190978 _Vladimir Joseph Stephan Orlovsky_, May 24 2011