A215288 - OEIS

%I #8 Apr 06 2021 20:41:48

%S 1,6,30,280,2100,23100,210210,2522520,25729704,325909584,3585005424,

%T 47117214144,546896235600,7383099180600,89212448432250,

%U 1229149289511000,15323394475903800,214527522662653200,2742051789669912720

%N 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 R. H. Hardin, <a href="/A215288/b215288.txt">Table of n, a(n) for n = 1..210</a>

%F f3=floor((n+1)/2),

%F f4=floor(n/2),

%F a(n) = A060854(2,f3)*A060854(2,f4)*binomial(2*f3+2*f4,2*f3).

%e Some solutions for n=5

%e ..2..x..4..x....0..x..3..x....2..x..3..x....0..x..5..x....1..x..4..x

%e ..x..0..x..1....x..2..x..5....x..0..x..4....x..1..x..3....x..0..x..6

%e ..3..x..7..x....1..x..6..x....5..x..6..x....6..x..7..x....2..x..5..x

%e ..x..6..x..9....x..4..x..7....x..1..x..8....x..2..x..4....x..3..x..8

%e ..5..x..8..x....8..x..9..x....7..x..9..x....8..x..9..x....7..x..9..x

%Y Column 4 of A215292.

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 07 2012