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 A289203 #12 Feb 16 2025 08:33:48
%S A289203 1,1,2,6,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
%T A289203 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,
%U A289203 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2
%N A289203 Number of maximum independent vertex sets in the n X n knight graph.
%H A289203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentVertexSet.html">Independent Vertex Set</a>
%H A289203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>
%H A289203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumIndependentVertexSet.html">Maximum Independent Vertex Set</a>
%H A289203 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F A289203 For n > 4, a(n) = ((-1)^n + 3)/2.
%F A289203 G.f.: (x*(-1 - x - x^2 - 5*x^3 + x^4 + 4*x^5))/(-1 + x^2).
%t A289203 Table[Length[With[{g = KnightTourGraph[n, n]}, FindIndependentVertexSet[g, Length /@ FindIndependentVertexSet[g], All]]], {n, 8}]
%t A289203 Table[Piecewise[{{1, n == 2}, {2, n == 3}, {6, n == 4}, {2, Mod[n, 2] == 0}, {1, Mod[n, 2] == 1}}], {n, 100}]
%t A289203 Table[Piecewise[{{1, n == 2}, {2, n == 3}, {6, n == 4}}, ((-1)^n + 3)/2], {n, 100}]
%t A289203 CoefficientList[Series[(-1 - x - x^2 - 5 x^3 + x^4 + 4 x^5)/(-1 + x^2), {x, 0, 20}],x]
%o A289203 (Python)
%o A289203 def A289203(n): return (1,1,2,6)[n-1] if n<5 else 2-(n&1) # _Chai Wah Wu_, Feb 12 2024
%Y A289203 Cf. A000034.
%K A289203 nonn,easy
%O A289203 1,3
%A A289203 _Eric W. Weisstein_, Jun 28 2017