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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
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
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.)