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A098604
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Triangle T(n,k) read by rows, for 1 <= k <= n: minimal number of knights needed to cover a k X n board.
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2
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1, 2, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 6, 4, 4, 4, 6, 8, 7, 6, 6, 6, 7, 8, 10, 8, 8, 8, 8, 8, 8, 11, 12, 9, 8, 8, 8, 8, 10, 12, 13, 14, 10, 8, 8, 8, 9, 12, 14, 14, 15, 16, 11, 8, 8, 8, 10, 12, 15, 16, 17, 19, 21, 12, 8, 8, 8, 10, 12, 16, 16, 18, 20, 22, 24, 13, 10, 10, 10, 12, 14
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| How many knights are needed to occupy or attack every square of a k X n board?
I do not know how many of these numbers have been proved to be optimal. - N. J. A. Sloane (njas(AT)research.att.com), Nov 08 2004.
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LINKS
| Lee Morgenstern, Knight Domination
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EXAMPLE
| Triangle begins:
1
2 4
3 4 4
4 4 4 4
5 4 4 4 5
6 4 4 4 6 8
7 6 6 6 7 8 10
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CROSSREFS
| See A006075 for the n X n case (the main diagonal). A006076 gives number of ways to cover an n X n board using the minimal number of knights.
Sequence in context: A069655 A004574 A073127 * A083172 A104148 A089169
Adjacent sequences: A098601 A098602 A098603 * A098605 A098606 A098607
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KEYWORD
| nonn,tabl,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Morgenstern's table extends a long way beyond what is shown here.
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