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A215295 Number of permutations of 0..floor((n*5-2)/2) on odd squares of an nX5 array such that each row and column of odd squares is increasing.

%I A215295 #6 Jul 22 2025 23:23:58
%S A215295 1,10,70,2100,23100,1051050,14294280,814773960,12547518984,
%T A215295 824551247520,13781785137120,999179422441200,17699749768958400,
%U A215295 1379105502831342000,25513451802379827000,2100607531729272423000,40191624107086745693400
%N A215295 Number of permutations of 0..floor((n*5-2)/2) on odd squares of an nX5 array such that each row and column of odd squares is increasing.
%C A215295 Column 5 of A215297
%H A215295 R. H. Hardin, <a href="/A215295/b215295.txt">Table of n, a(n) for n = 1..210</a>
%F A215295 f3=floor((n+1)/2)
%F A215295 f4=floor(n/2)
%F A215295 a(n) = A060854(2,f3)*A060854(3,f4)*binomial(2*f3+3*f4,2*f3)
%e A215295 Some solutions for n=5
%e A215295 ..x..2..x..6..x....x..1..x..5..x....x..0..x..5..x....x..0..x..2..x
%e A215295 ..0..x..3..x..4....0..x..2..x..7....2..x..4..x.10....3..x..6..x..8
%e A215295 ..x..5..x.10..x....x..3..x..9..x....x..1..x..8..x....x..1..x..7..x
%e A215295 ..1..x..7..x..8....4..x..6..x.11....6..x..7..x.11....4..x..9..x.11
%e A215295 ..x..9..x.11..x....x..8..x.10..x....x..3..x..9..x....x..5..x.10..x
%K A215295 nonn
%O A215295 1,2
%A A215295 _R. H. Hardin_ Aug 07 2012