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 A110293 #39 Jul 10 2025 04:55:58
%S A110293 1,7,13,97,181,1351,2521,18817,35113,262087,489061,3650401,6811741,
%T A110293 50843527,94875313,708158977,1321442641,9863382151,18405321661,
%U A110293 137379191137,256353060613,1913445293767,3570537526921,26650854921601,49731172316281,371198523608647,692665874901013
%N A110293 a(2*n) = A001570(n), a(2*n+1) = A011943(n+1).
%C A110293 See also A110294 (compare program code).
%H A110293 Colin Barker, <a href="/A110293/b110293.txt">Table of n, a(n) for n = 0..1000</a>
%H A110293 Yurii S. Bystryk, Vitalii L. Denysenko, and Volodymyr I. Ostryk, <a href="http://dx.doi.org/10.13140/RG.2.2.16511.73129">Lune and Lens Sequences</a>, ResearchGate preprint, 2024. See pp. 30, 56.
%H A110293 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,14,0,-1).
%F A110293 G.f.: (1+7*x-x^2-x^3) / ((1-4*x+x^2)*(1+4*x+x^2)).
%F A110293 a(2*n+1) = (a(2*n) + a(2*n+2))/2 and see A232765 for Diophantine equation that produces a sequence related to a(n). - _Richard R. Forberg_, Nov 30 2013
%F A110293 From _Colin Barker_, Nov 01 2016: (Start)
%F A110293 a(n) = (3-(-1)^n)*((-3+2*sqrt(3))*(2-sqrt(3))^n + (3+2*sqrt(3))*(2+sqrt(3))^n )/(8*sqrt(3)).
%F A110293 a(n) = 14*a(n-2) - a(n-4) for n>3. (End)
%F A110293 a(n) = (1/4)*(3 - (-1)^n)*(2*A001353(n) - A001353(n-1)). - _G. C. Greubel_, Jan 04 2023
%p A110293 seriestolist(series((1+7*x-x^2-x^3)/((1-4*x+x^2)*(1+4*x+x^2)), x=0, 25));
%t A110293 CoefficientList[Series[(1+7x-x^2-x^3)/((1-4x+x^2)(1+4x+x^2)), {x, 0, 25}], x] (* _Michael De Vlieger_, Nov 01 2016 *)
%o A110293 (PARI) Vec((1+7*x-x^2-x^3)/((1-4*x+x^2)*(1+4*x+x^2)) + O(x^30)) \\ _Colin Barker_, Nov 01 2016
%o A110293 (Magma)
%o A110293 A001353:= func< n | Evaluate(ChebyshevSecond(n+1), 2) >;
%o A110293 [(3-(-1)^n)*(2*A001353(n) - A001353(n-1))/4: n in [0..40]]; // _G. C. Greubel_, Jan 04 2023
%o A110293 (SageMath)
%o A110293 def A001353(n): return chebyshev_U(n,2)
%o A110293 [(3-(-1)^n)*(2*A001353(n) - A001353(n-1))/4 for n in range(41)] # _G. C. Greubel_, Jan 04 2023
%Y A110293 Cf. A001353, A001570, A011943, A110294, A232765.
%K A110293 easy,nonn
%O A110293 0,2
%A A110293 _Creighton Dement_, Jul 18 2005