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

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, 8, 12, 16, 20, 24, 28, 32, 9, 10, 14, 18, 23, 27, 32, 36, 41, 10, 12, 15, 20, 25, 30, 35, 40, 45, 50, 11, 12, 17, 22, 28, 33, 39, 44, 50, 55, 61

Offset: 1

Author

Eric W. Weisstein, Jun 01 2017

Keywords

• nonn
• tabl

Examples

			1;
2, 4;
3, 4, 5;
4, 4, 6, 8;
5, 6, 8, 10, 13;
6, 8, 9, 12, 15, 18;
		

Links

• Eric Weisstein's World of Mathematics, Independence Number
• Eric Weisstein's World of Mathematics, Knight Graph

Crossrefs

Cf. A030978 (n X n knight graphs).

Cf. A201629 (2 X n knight graphs).

Programs

Mathematica

Table[IndependenceNumber[KnightTourGraph[m, n]], {n, 10}, {m, n}] // Flatten
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

Formula

T(n,n) = A030978(n).

T(n,2) = A201629(n+1).