A215293 - OEIS

%I #10 Apr 03 2021 22:01:39

%S 1,2,6,280,23100,85765680,577185873264,346915095471584640,

%T 381134230556959188429120,62144711688730139887005809020800,

%U 18592619468814454675301397184588597886400

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

%H R. H. Hardin, <a href="/A215293/b215293.txt">Table of n, a(n) for n = 1..40</a>

%F f1=floor(n/2),

%F f2=floor((n+1)/2),

%F T(n,k)=A060854(f1,f2)*A060854(f2,f1)*binomial(f1*f2+f2*f1,f1*f2).

%e Some solutions for n=5

%e ..x..0..x..4..x....x..4..x..6..x....x..1..x..6..x....x..0..x..6..x

%e ..1..x..3..x..7....0..x..1..x..9....0..x..2..x..3....3..x..4..x..9

%e ..x..2..x..5..x....x..5..x..8..x....x..7..x..8..x....x..1..x..7..x

%e ..8..x..9..x.10....2..x..3..x.10....4..x..5..x.11....5..x..8..x.11

%e ..x..6..x.11..x....x..7..x.11..x....x..9..x.10..x....x..2..x.10..x

%Y Diagonal of A215297.

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 07 2012