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%I #4 Aug 07 2012 11:35:45
%S 1,10,140,2100,60060,1051050,42882840,814773960,41227562376,
%T 824551247520,48236247979920,999179422441200,64899082486180800,
%U 1379105502831342000,96951116849043342600,2100607531729272423000,157112712418611824074200
%N Number of permutations of 0..floor((n*5-1)/2) on even squares of an nX5 array such that each row and column of even squares is increasing
%C Column 5 of A215292
%H R. H. Hardin, <a href="/A215289/b215289.txt">Table of n, a(n) for n = 1..210</a>
%F f3=floor((n+1)/2)
%F f4=floor(n/2)
%F a(n) = A060854(3,f3)*A060854(2,f4)*binomial(3*f3+2*f4,3*f3)
%e Some solutions for n=5
%e ..0..x..2..x..6....1..x..2..x..6....0..x..3..x..9....0..x..1..x..8
%e ..x..3..x..4..x....x..0..x..4..x....x..2..x..4..x....x..3..x..6..x
%e ..1..x..7..x.10....7..x..9..x.11....1..x..7..x.11....2..x..4..x..9
%e ..x..5..x.11..x....x..3..x..5..x....x..5..x..8..x....x..7..x.10..x
%e ..8..x..9..x.12....8..x.10..x.12....6..x.10..x.12....5..x.11..x.12
%K nonn
%O 1,2
%A _R. H. Hardin_ Aug 07 2012