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A215291 Number of permutations of 0..floor((n*7-1)/2) on even squares of an nX7 array such that each row and column of even squares is increasing.

%I A215291 #6 Jul 22 2025 23:23:43
%S A215291 1,35,2310,210210,42882840,5703417720,2061378118800,337653735859440,
%T A215291 173457547735792320,32436561426593163840,21174123919831066023840,
%U A215291 4340695403565368534887200,3373030378241974592216989200
%N A215291 Number of permutations of 0..floor((n*7-1)/2) on even squares of an nX7 array such that each row and column of even squares is increasing.
%C A215291 Column 7 of A215292
%H A215291 R. H. Hardin, <a href="/A215291/b215291.txt">Table of n, a(n) for n = 1..210</a>
%F A215291 f3=floor((n+1)/2)
%F A215291 f4=floor(n/2)
%F A215291 a(n) = A060854(4,f3)*A060854(3,f4)*binomial(4*f3+3*f4,4*f3)
%e A215291 Some solutions for n=3
%e A215291 ..0..x..3..x..5..x..6....0..x..1..x..2..x..3....1..x..2..x..3..x..5
%e A215291 ..x..1..x..8..x.10..x....x..5..x..8..x.10..x....x..0..x..6..x.10..x
%e A215291 ..2..x..4..x..7..x..9....4..x..6..x..7..x..9....4..x..7..x..8..x..9
%K A215291 nonn
%O A215291 1,2
%A A215291 _R. H. Hardin_ Aug 07 2012