A215292 T(n,k)=Number of permutations of 0..floor((n*k-1)/2) on even squares of an nXk array such that each row and column of even squares is increasing.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 6, 10, 6, 1, 1, 10, 30, 30, 10, 1, 1, 20, 140, 280, 140, 20, 1, 1, 35, 420, 2100, 2100, 420, 35, 1, 1, 70, 2310, 23100, 60060, 23100, 2310, 70, 1, 1, 126, 6930, 210210, 1051050, 1051050, 210210, 6930, 126, 1, 1, 252, 42042, 2522520

Offset: 1

Author

R. H. Hardin Aug 07 2012

Keywords

• nonn
• tabl

Comments

Table starts

.1...1.....1........1...........1..............1..................1

.1...2.....3........6..........10.............20.................35

.1...3....10.......30.........140............420...............2310

.1...6....30......280........2100..........23100.............210210

.1..10...140.....2100.......60060........1051050...........42882840

.1..20...420....23100.....1051050.......85765680.........5703417720

.1..35..2310...210210....42882840.....5703417720......2061378118800

.1..70..6930..2522520...814773960...577185873264....337653735859440

.1.126.42042.25729704.41227562376.48236247979920.173457547735792320

Examples

			Some solutions for n=5 k=4
..1..x..2..x....0..x..6..x....1..x..6..x....1..x..4..x....0..x..6..x
..x..0..x..4....x..3..x..4....x..0..x..3....x..0..x..3....x..1..x..2
..3..x..8..x....1..x..7..x....4..x..7..x....2..x..7..x....4..x..7..x
..x..6..x..7....x..5..x..8....x..2..x..8....x..5..x..6....x..3..x..9
..5..x..9..x....2..x..9..x....5..x..9..x....8..x..9..x....5..x..8..x
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1000

Crossrefs

Column 2 is A001405

Formula

f1=floor((k+1)/2)

f2=floor(k/2)

f3=floor((n+1)/2)

f4=floor(n/2)

T(n,k)=A060854(f1,f3)*A060854(f2,f4)*binomial(f1*f3+f2*f4,f1*f3)