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A181501
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Triangle read by rows: number of solutions of n queens problem for given n and given number of connection components of conflict constellation
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4
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0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 10, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 28, 0, 4, 8, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 8, 272, 56, 16, 0, 0, 0, 0, 0, 0, 96, 344, 240, 44, 0, 0, 0, 0, 0, 0
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OFFSET
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0,13
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COMMENTS
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The rightmost part of the triangle contains only zeros. As any connection component needs at least two queens, the number of connection components of a solution is always less than or equal to n.
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LINKS
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FORMULA
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Row sum =A000170 (number of n queens placements)
Column 0 has same values as A007705 (torus n queens solutions)
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EXAMPLE
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Triangle begins:
0;
1, 0;
0, 0, 0;
0, 0, 0, 0;
0, 0, 2, 0, 0;
10, 0, 0, 0, 0, 0;
0, 4, 0, 0, 0, 0, 0;
28, 0, 4, 8, 0, 0, 0, 0;
for n=4, there are only the two solutions 2-4-1-3 and 3-1-4-2. Both have two connection components in the conflicts graph. So, the terms for n=4 are 0, 0, 2 (the two cited above), 0 and 0. These are members 10 to 15 of the sequence.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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