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 A046163 #30 Feb 16 2025 08:32:39
%S A046163 1,7,13,7,31,43,19,73,91,37,133,157,61,211,241,91,307,343,127,421,463,
%T A046163 169,553,601,217,703,757,271,871,931,331,1057,1123,397,1261,1333,469,
%U A046163 1483,1561,547,1723,1807,631,1981,2071,721,2257,2353,817,2551,2653
%N A046163 Reduced denominators of (n-1)^2/(n^2 + n + 1).
%C A046163 Arises in Routh's theorem.
%H A046163 G. C. Greubel, <a href="/A046163/b046163.txt">Table of n, a(n) for n = 1..5000</a>
%H A046163 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RouthsTheorem.html">Routh's Theorem</a>.
%H A046163 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3,0,0,-3,0,0,1).
%F A046163 G.f.: x*(1 + 7*x + 13*x^2 + 4*x^3 + 10*x^4 + 4*x^5 + x^6 + x^7 + x^8)/(1 - x^3)^3.
%F A046163 From _Amiram Eldar_, Aug 11 2022: (Start)
%F A046163 a(n) = numerator((n^2 + n + 1)/3).
%F A046163 Sum_{n>=1} 1/a(n) = (2*tanh(Pi/(2*sqrt(3))) + 3*tanh(sqrt(3)*Pi/2))*Pi/(3*sqrt(3)) - 1. (End)
%t A046163 a[n_] := Denominator[(n - 1)^2/(n^2 + n + 1)]; Array[a, 50] (* _Amiram Eldar_, Aug 11 2022 *)
%o A046163 (Magma) [Denominator((n-1)^2/(n^2+n+1)): n in [1..70]]; // _G. C. Greubel_, Oct 27 2022
%o A046163 (SageMath) [denominator((n-1)^2/(n^2+n+1)) for n in range(1,71)] # _G. C. Greubel_, Oct 27 2022
%Y A046163 Cf. A046162 (numerators).
%K A046163 nonn,easy
%O A046163 1,2
%A A046163 _Eric W. Weisstein_