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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 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 22 20:51 EDT 2019. Contains 325226 sequences. (Running on oeis4.)