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%I #7 Jun 22 2022 00:41:48
%S 23244,1373400,73775908,2902004018,109885347688,3518676186849,
%T 109442756670711,3115212983893648,86726190046550479,
%U 2304039589889181877,60300435912522661946,1540435957552411019321,39002535056386537871612
%N Number of (n+1) X 4 0..3 arrays with the permanents of 2 X 2 subblocks nondecreasing rightwards and downwards.
%C Column 3 of A205181.
%H R. H. Hardin, <a href="/A205176/b205176.txt">Table of n, a(n) for n = 1..210</a>
%e Some solutions for n=4
%e ..3..3..1..1....1..0..0..0....1..3..2..0....1..1..0..3....1..0..3..3
%e ..1..0..1..2....0..0..2..1....0..0..0..1....2..1..3..3....1..3..2..2
%e ..1..3..1..2....0..1..3..1....0..1..3..3....3..0..3..2....1..1..3..3
%e ..1..2..1..3....3..3..1..3....3..2..3..0....2..1..3..3....1..3..2..3
%e ..2..1..2..1....0..1..3..1....3..1..3..3....0..2..2..3....1..1..3..3
%Y Cf. A205181.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 22 2012