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%I
%S 14178,102445,545662,2430950,9496395,33351260,107058241,318063303,
%T 883398416,2312834051,5747404508,13634816674,31030883261,68030181122,
%U 144179542873,296289041222,591935421670,1152308627603,2190104262402
%N Number of (n+2)X3 0..3 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order
%C Column 1 of A184574
%H R. H. Hardin, <a href="/A184566/b184566.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = (1/121645100408832000)*n^19
%F + (53/3201186852864000)*n^18
%F + (5743/2134124568576000)*n^17
%F + (12931/62768369664000)*n^16
%F + (621041/62768369664000)*n^15
%F + (10734523/31384184832000)*n^14
%F + (1720232317/188305108992000)*n^13
%F + (127448011/658409472000)*n^12
%F + (6294370109/1931334451200)*n^11
%F + (18970604773/438939648000)*n^10
%F + (4321841102639/9656672256000)*n^9
%F + (17491957547611/4828336128000)*n^8
%F + (1086794057312713/47076277248000)*n^7
%F + (2752481070552527/23538138624000)*n^6
%F + (1237909924891457/2615348736000)*n^5
%F + (1921023328483453/1307674368000)*n^4
%F + (249101413506019/77189112000)*n^3
%F + (12857906145353/2806876800)*n^2
%F + (288855292519/77597520)*n
%F + 561
%e Some solutions for 4X3
%e ..0..1..3....0..1..1....0..0..2....0..0..0....0..1..3....0..0..3....0..1..1
%e ..0..2..3....0..1..2....0..1..2....1..1..3....0..3..3....0..1..3....1..1..1
%e ..3..2..3....2..2..3....3..0..0....1..2..0....2..0..0....0..3..3....1..2..3
%e ..3..3..1....2..3..1....3..3..1....3..0..0....3..1..3....2..0..1....2..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 17 2011
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