%I #5 Mar 31 2012 12:36:46

%S 4,131,9260,408599,8002304,91893727,729771318,4412536785,21616887220,

%T 89573637672,323882961806,1046082959963,3072688515840,8324694513560,

%U 21037789421604,50045713319142,112903666194660,243057004503527

%N Number of nX4 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards

%C Column 4 of A201981

%H R. H. Hardin, <a href="/A201977/b201977.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/800296713216000)*n^18 + (1/279189504000)*n^17 + (95419/31384184832000)*n^16 + (61393/58118860800)*n^15 + (13474067/89159616000)*n^14 + (1944881051/249080832000)*n^13 + (287748203459/3621252096000)*n^12 - (9381832307/5748019200)*n^11 + (565158095051/109734912000)*n^10 + (1007220012059/8128512000)*n^9 - (4235093372549201/2414168064000)*n^8 + (1553448377549/136857600)*n^7 - (503383886122557787/11769069312000)*n^6 + (655941897398819/7185024000)*n^5 - (4125496035344653/59439744000)*n^4 - (45705619838101/302702400)*n^3 + (7044605010470827/15437822400)*n^2 - (1427735531371/3063060)*n + 171950

%e Some solutions for n=3

%e ..0..0..3..3....0..2..3..3....0..0..0..3....0..1..2..3....1..3..3..3

%e ..1..3..0..2....2..0..0..1....1..1..2..1....1..3..1..0....3..0..0..2

%e ..3..2..2..1....3..3..1..0....3..3..1..1....2..0..0..0....3..2..2..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 07 2011