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A215296 Number of permutations of 0..floor((n*7-2)/2) on odd squares of an nX7 array such that each row and column of odd squares is increasing.

%I A215296 #6 Jul 22 2025 23:24:05
%S A215296 1,35,1050,210210,14294280,5703417720,577185873264,337653735859440,
%T A215296 43364386933948080,32436561426593163840,4886336289191784467040,
%U A215296 4340695403565368534887200,733267473530864041786302000
%N A215296 Number of permutations of 0..floor((n*7-2)/2) on odd squares of an nX7 array such that each row and column of odd squares is increasing.
%C A215296 Column 7 of A215297
%H A215296 R. H. Hardin, <a href="/A215296/b215296.txt">Table of n, a(n) for n = 1..210</a>
%F A215296 f3=floor((n+1)/2)
%F A215296 f4=floor(n/2)
%F A215296 a(n) = A060854(3,f3)*A060854(4,f4)*binomial(3*f3+4*f4,3*f3)
%e A215296 Some solutions for n=3
%e A215296 ..x..0..x..1..x..3..x....x..0..x..2..x..5..x....x..0..x..1..x..3..x
%e A215296 ..2..x..4..x..6..x..9....3..x..6..x..8..x..9....5..x..6..x..8..x..9
%e A215296 ..x..5..x..7..x..8..x....x..1..x..4..x..7..x....x..2..x..4..x..7..x
%K A215296 nonn
%O A215296 1,2
%A A215296 _R. H. Hardin_ Aug 07 2012