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 A110309 #13 Jan 03 2023 02:07:31
%S A110309 1,-3,12,-57,275,-1320,6325,-30303,145188,-695637,3332999,-15969360,
%T A110309 76513801,-366599643,1756484412,-8415822417,40322627675,-193197315960,
%U A110309 925663952125,-4435122444663,21249948271188,-101814618911277,487823146285199,-2337301112514720
%N A110309 Expansion of (1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)).
%H A110309 Colin Barker, <a href="/A110309/b110309.txt">Table of n, a(n) for n = 0..1000</a>
%H A110309 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-7,-6,-1).
%F A110309 a(n+2) = - 5*a(n+1) - a(n) + (-1)^n*A109265(n+3).
%F A110309 a(n) = -6*a(n-1) - 7*a(n-2) - 6*a(n-3) - a(n-4) for n>3. - _Colin Barker_, Apr 30 2019
%F A110309 a(n) = (1/2)*(ChebyshevU(n, -5/2) + ChebyshevU(n, -1/2)). - _G. C. Greubel_, Jan 03 2023
%p A110309 seriestolist(series((1+3*x+x^2)/((x^2+5*x+1)*(x^2+x+1)), x=0,25));
%t A110309 LinearRecurrence[{-6,-7,-6,-1}, {1,-3,12,-57}, 40] (* _G. C. Greubel_, Jan 03 2023 *)
%o A110309 (PARI) Vec((1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)) + O(x^25)) \\ _Colin Barker_, Apr 30 2019
%o A110309 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x+x^2)/((1+x+x^2)*(1+5*x+x^2)) )); // _G. C. Greubel_, Jan 03 2023
%o A110309 (SageMath)
%o A110309 def A110309(n): return (1/2)*(chebyshev_U(n,-5/2)+chebyshev_U(n,-1/2))
%o A110309 [A110309(n) for n in range(41)] # _G. C. Greubel_, Jan 03 2023
%Y A110309 Cf. A004253, A049347, A109265, A110307, A110308, A110310, A110311.
%K A110309 easy,sign
%O A110309 0,2
%A A110309 _Creighton Dement_, Jul 19 2005