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

1,12

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