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 A215870 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. 11
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS 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 LINKS R. H. Hardin, Table of n, a(n) for n = 1..125 FORMULA Empirical for column k: k=4: a(n) = 2*a(n-2), A016116. 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). EXAMPLE 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 CROSSREFS Column 5 is A026395(n-1). Row 2 is A000108(floor(n/2)). Even squares: A215788. Sequence in context: A333159 A008327 A133687 * A097587 A001179 A001876 Adjacent sequences: A215867 A215868 A215869 * A215871 A215872 A215873 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Aug 25 2012 STATUS approved

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Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)