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 A215788 T(n,k)=Number of permutations of 0..floor((n*k-1)/2) on even squares of an nXk array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing 11
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 5, 12, 10, 4, 1, 1, 1, 1, 5, 42, 29, 25, 4, 1, 1, 1, 1, 14, 110, 262, 189, 50, 8, 1, 1, 1, 1, 14, 462, 932, 2465, 458, 125, 8, 1, 1, 1, 1, 42, 1274, 11694, 26451, 15485, 2988, 250, 16, 1, 1, 1, 1, 42, 6006 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,17 COMMENTS Table starts .1.1.1..1....1......1........1..........1...........1...........1...........1 .1.1.1..1....2......2........5..........5..........14..........14..........42 .1.1.1..2....5.....12.......42........110.........462........1274........6006 .1.1.1..2...10.....29......262........932.......11694.......46988......727846 .1.1.1..4...25....189.....2465......26451......530429.....7027942...187205626 .1.1.1..4...50....458....15485.....234217....14296434...297246092.26970790176 .1.1.1..8..125...2988...146205....6812794...673507749.48337803306 .1.1.1..8..250...7241...918637...60485308.18255280444 .1.1.1.16..625..47241..8674386.1761748159 .1.1.1.16.1250.114482.54503318 .1.1.1.32.3125.746892 .1.1.1.32.6250 LINKS R. H. Hardin, Table of n, a(n) for n = 1..140 FORMULA Empirical for column k: k=4: a(n) = 2*a(n-2) k=5: a(n) = 5*a(n-2) k=6: a(n) = 16*a(n-2) -3*a(n-4) k=7: a(n) = 61*a(n-2) -99*a(n-4) -2*a(n-6) 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=7 k=4 ..0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x ..x..2..x..3....x..2..x..4....x..2..x..4....x..2..x..3....x..2..x..3 ..4..x..5..x....3..x..5..x....3..x..5..x....4..x..5..x....4..x..5..x ..x..6..x..8....x..6..x..8....x..6..x..8....x..6..x..7....x..6..x..7 ..7..x..9..x....7..x..9..x....7..x..9..x....8..x..9..x....8..x..9..x ..x.10..x.12....x.10..x.12....x.10..x.11....x.10..x.12....x.10..x.11 .11..x.13..x...11..x.13..x...12..x.13..x...11..x.13..x...12..x.13..x CROSSREFS Column 5 is A026383(n-1) Row 2 is A000108(floor((n-1)/2)) Odd squares: A215870 Sequence in context: A071838 A157896 A156072 * A060990 A276309 A165031 Adjacent sequences:  A215785 A215786 A215787 * A215789 A215790 A215791 KEYWORD nonn,tabl AUTHOR R. H. Hardin Aug 23 2012 STATUS approved

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Last modified December 4 13:29 EST 2021. Contains 349526 sequences. (Running on oeis4.)