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.

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

Offset: 1

Author

R. H. Hardin, Aug 25 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..125

Crossrefs

Column 5 is A026395(n-1).

Row 2 is A000108(floor(n/2)).

Even squares: A215788.

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).