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A215288 Number of permutations of 0..floor((n*4-1)/2) on even squares of an n X 4 array such that each row and column of even squares is increasing.

%I A215288 #8 Apr 06 2021 20:41:48
%S A215288 1,6,30,280,2100,23100,210210,2522520,25729704,325909584,3585005424,
%T A215288 47117214144,546896235600,7383099180600,89212448432250,
%U A215288 1229149289511000,15323394475903800,214527522662653200,2742051789669912720
%N A215288 Number of permutations of 0..floor((n*4-1)/2) on even squares of an n X 4 array such that each row and column of even squares is increasing.
%H A215288 R. H. Hardin, <a href="/A215288/b215288.txt">Table of n, a(n) for n = 1..210</a>
%F A215288 f3=floor((n+1)/2),
%F A215288 f4=floor(n/2),
%F A215288 a(n) = A060854(2,f3)*A060854(2,f4)*binomial(2*f3+2*f4,2*f3).
%e A215288 Some solutions for n=5
%e A215288 ..2..x..4..x....0..x..3..x....2..x..3..x....0..x..5..x....1..x..4..x
%e A215288 ..x..0..x..1....x..2..x..5....x..0..x..4....x..1..x..3....x..0..x..6
%e A215288 ..3..x..7..x....1..x..6..x....5..x..6..x....6..x..7..x....2..x..5..x
%e A215288 ..x..6..x..9....x..4..x..7....x..1..x..8....x..2..x..4....x..3..x..8
%e A215288 ..5..x..8..x....8..x..9..x....7..x..9..x....8..x..9..x....7..x..9..x
%Y A215288 Column 4 of A215292.
%K A215288 nonn
%O A215288 1,2
%A A215288 _R. H. Hardin_, Aug 07 2012