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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.

%I A215292 #6 Jul 22 2025 23:23:50
%S A215292 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,
%T A215292 1,35,420,2100,2100,420,35,1,1,70,2310,23100,60060,23100,2310,70,1,1,
%U A215292 126,6930,210210,1051050,1051050,210210,6930,126,1,1,252,42042,2522520
%N 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.
%C A215292 Table starts
%C A215292 .1...1.....1........1...........1..............1..................1
%C A215292 .1...2.....3........6..........10.............20.................35
%C A215292 .1...3....10.......30.........140............420...............2310
%C A215292 .1...6....30......280........2100..........23100.............210210
%C A215292 .1..10...140.....2100.......60060........1051050...........42882840
%C A215292 .1..20...420....23100.....1051050.......85765680.........5703417720
%C A215292 .1..35..2310...210210....42882840.....5703417720......2061378118800
%C A215292 .1..70..6930..2522520...814773960...577185873264....337653735859440
%C A215292 .1.126.42042.25729704.41227562376.48236247979920.173457547735792320
%H A215292 R. H. Hardin, <a href="/A215292/b215292.txt">Table of n, a(n) for n = 1..1000</a>
%F A215292 f1=floor((k+1)/2)
%F A215292 f2=floor(k/2)
%F A215292 f3=floor((n+1)/2)
%F A215292 f4=floor(n/2)
%F A215292 T(n,k)=A060854(f1,f3)*A060854(f2,f4)*binomial(f1*f3+f2*f4,f1*f3)
%e A215292 Some solutions for n=5 k=4
%e A215292 ..1..x..2..x....0..x..6..x....1..x..6..x....1..x..4..x....0..x..6..x
%e A215292 ..x..0..x..4....x..3..x..4....x..0..x..3....x..0..x..3....x..1..x..2
%e A215292 ..3..x..8..x....1..x..7..x....4..x..7..x....2..x..7..x....4..x..7..x
%e A215292 ..x..6..x..7....x..5..x..8....x..2..x..8....x..5..x..6....x..3..x..9
%e A215292 ..5..x..9..x....2..x..9..x....5..x..9..x....8..x..9..x....5..x..8..x
%Y A215292 Column 2 is A001405
%K A215292 nonn,tabl
%O A215292 1,5
%A A215292 _R. H. Hardin_ Aug 07 2012