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.

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

Offset: 1

Author

R. H. Hardin Aug 23 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..140

Crossrefs

Column 5 is A026383(n-1)

Row 2 is A000108(floor((n-1)/2))

Odd squares: A215870

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)