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

1,2

Links

Table of n, a(n) for n=1..66.

Eric Weisstein's World of Mathematics, Independence Number

Eric Weisstein's World of Mathematics, Knight Graph

Formula

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

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

Example

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

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

Crossrefs

Cf. A030978 (n X n knight graphs).

Cf. A201629 (2 X n knight graphs).

Sequence in context: A274047 A226644 A083172 * A369430 A360691 A302707

Adjacent sequences: A287794 A287795 A287796 * A287798 A287799 A287800

Keyword

nonn,tabl

Author

Eric W. Weisstein, Jun 01 2017

Status

approved