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A215870
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T(n,k) = Number of permutations of 0..floor((n*k-2)/2) on odd squares of an n X k array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.
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11
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 5, 4, 4, 1, 1, 1, 1, 5, 12, 10, 4, 1, 1, 1, 1, 14, 29, 78, 20, 8, 1, 1, 1, 1, 14, 110, 262, 189, 50, 8, 1, 1, 1, 1, 42, 290, 3001, 1642, 1233, 100, 16, 1, 1, 1, 1, 42, 1274, 11694, 26451, 15485, 2988, 250, 16, 1, 1, 1, 1, 132
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OFFSET
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1,12
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COMMENTS
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Table starts
.1.1.1..1....1......1.......1.........1.........1..........1........1
.1.1.1..2....2......5.......5........14........14.........42.......42
.1.1.1..2....4.....12......29.......110.......290.......1274.....3532
.1.1.1..4...10.....78.....262......3001.....11694.....170594...727846
.1.1.1..4...20....189....1642.....26451....307874....7027942.98057806
.1.1.1..8...50...1233...15485....767560..14296434.1124811332
.1.1.1..8..100...2988...97289...6812794.386699176
.1.1.1.16..250..19494..918637.198409297
.1.1.1.16..500..47241.5772013
.1.1.1.32.1250.308205
.1.1.1.32.2500
.1.1.1.64
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LINKS
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FORMULA
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Empirical for column k:
k=5: a(n) = 5*a(n-2) for n>3, A026395.
k=6: a(n) = 16*a(n-2) -3*a(n-4), A215866.
k=7: a(n) = 61*a(n-2) -99*a(n-4) -2*a(n-6), A215867.
k=8: a(n) = 272*a(n-2) -3439*a(n-4) -3336*a(n-6) +140*a(n-8).
k=9: a(n) = 1385*a(n-2) -131648*a(n-4) -318070*a(n-6) -4160916*a(n-8) -1097892*a(n-10) +648*a(n-12).
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EXAMPLE
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Some solutions for n=6, k=4:
..x..0..x..1....x..0..x..2....x..0..x..2....x..0..x..1....x..0..x..1
..2..x..3..x....1..x..3..x....1..x..3..x....2..x..3..x....2..x..3..x
..x..4..x..5....x..4..x..6....x..4..x..5....x..4..x..6....x..4..x..6
..6..x..7..x....5..x..7..x....6..x..7..x....5..x..7..x....5..x..7..x
..x..8..x.10....x..8..x.10....x..8..x.10....x..8..x.10....x..8..x..9
..9..x.11..x....9..x.11..x....9..x.11..x....9..x.11..x...10..x.11..x
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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