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

1,5

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

Links

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

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)

Example

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

Crossrefs

Column 2 is A001405

Sequence in context: A181039 A215297 A225910 * A124975 A171246 A129439

Adjacent sequences: A215289 A215290 A215291 * A215293 A215294 A215295

Keyword

nonn,tabl

Author

R. H. Hardin Aug 07 2012

Status

approved