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A287797 Triangle read by rows: T(n,k) gives the independence number of the k X n knight graph.

%I A287797 #7 Feb 16 2025 08:33:47
%S A287797 1,2,4,3,4,5,4,4,6,8,5,6,8,10,13,6,8,9,12,15,18,7,8,11,14,18,21,25,8,
%T A287797 8,12,16,20,24,28,32,9,10,14,18,23,27,32,36,41,10,12,15,20,25,30,35,
%U A287797 40,45,50,11,12,17,22,28,33,39,44,50,55,61
%N A287797 Triangle read by rows: T(n,k) gives the independence number of the k X n knight graph.
%H A287797 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependenceNumber.html">Independence Number</a>
%H A287797 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>
%F A287797 T(n,n) = A030978(n).
%F A287797 T(n,2) = A201629(n+1).
%e A287797 1;
%e A287797 2, 4;
%e A287797 3, 4, 5;
%e A287797 4, 4, 6, 8;
%e A287797 5, 6, 8, 10, 13;
%e A287797 6, 8, 9, 12, 15, 18;
%t A287797 Table[IndependenceNumber[KnightTourGraph[m, n]], {n, 10}, {m, n}] // Flatten
%t A287797 Table[Piecewise[{{Max[m, n], Min[m, n] == 1}, {Max[m, n] + 1, Min[m, n] == 2 && Mod[Max[m, n], 2] == 1}, {4 Round[(Max[m, n] + 1)/4], Min[m, n] == 2 && Mod[Max[m, n], 2] == 0}, {m n/2, Mod[m n, 2] == 0}, {(m n + 1)/2, Mod[m n, 2] == 1}}], {n, 10}, {m, n}] // Flatten
%Y A287797 Cf. A030978 (n X n knight graphs).
%Y A287797 Cf. A201629 (2 X n knight graphs).
%K A287797 nonn,tabl
%O A287797 1,2
%A A287797 _Eric W. Weisstein_, Jun 01 2017