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 A356569 #17 Aug 15 2022 10:27:33
%S A356569 4,2,16,38,164,522,1936,6638,23684,82802,292496,1027798,3621284,
%T A356569 12741562,44862736,157904478,555880964,1956721762,6888057616,
%U A356569 24246779398,85352580004,300452999402,1057639862416
%N A356569 Sums of powers of roots of x^4 - 2*x^3 - 6*x^2 + 2*x + 1.
%C A356569 The four roots of x^4 - 2*x^3 - 6*x^2 + 2*x + 1, in order from smallest to largest, are c1 = sec(17*Pi/20)/sqrt(2) - 1, c2 = sec(Pi/20)/sqrt(2) - 1 = -A158934, c3 = sec(7*Pi/20)/sqrt(2) - 1, and c4 = sec(9*Pi/20)/sqrt(2) - 1.
%H A356569 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,6,-2,-1).
%F A356569 a(n) = 2*a(n-1) + 6*a(n-2) - 2*a(n-3) - a(n-4).
%F A356569 G.f.: 2*(2-3*x-6*x^2+x^3)/(1-2*x-6*x^2+2*x^3+x^4).
%F A356569 a(n) = b(n+1) + 6*b(n) - 3*b(n-1) - 2*b(n-2) for b(n) = A192380(n).
%e A356569 a(3) = (-1.7936045...)^3 + (-0.28407904...)^3 + (0.55753652...)^3 + (3.5201470...)^3 = 38, as expected.
%t A356569 Table[Sum[(Sec[k Pi/20]/Sqrt[2] - 1)^n, {k, {1, 7, 9, 17}}], {n, 0, 30}] // Round
%o A356569 (PARI) polsym(x^4 - 2*x^3 - 6*x^2 + 2*x + 1, 22) \\ _Joerg Arndt_, Aug 14 2022
%Y A356569 Cf. A192380, A158934 (-c2).
%K A356569 nonn,easy
%O A356569 0,1
%A A356569 _Greg Dresden_ and _Ding Hao_, Aug 12 2022