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%I #4 Jun 25 2013 21:00:03
%S 15,120,608,2820,11325,40431,130479,385529,1054857,2699060,6512038,
%T 14918723,32643565,68558024,138781999,271754453,516328629,954420655,
%U 1720389300,3030202067,5224614220,8832133194,14659559110,23920501241
%N Number of nX3 0..4 arrays of sums of 2X2 subblocks of some (n+1)X4 binary array with rows and columns of the latter in lexicographically nondecreasing order
%C Column 3 of A226992
%H R. H. Hardin, <a href="/A226989/b226989.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/1307674368000)*n^15 + (1/10897286400)*n^14 + (47/9340531200)*n^13 + (79/479001600)*n^12 + (2341/653184000)*n^11 + (2369/43545600)*n^10 + (136267/228614400)*n^9 + (1466509/304819200)*n^8 + (37910533/1306368000)*n^7 + (1168211/8709120)*n^6 + (362956849/718502400)*n^5 + (181454291/119750400)*n^4 + (8088745109/2270268000)*n^3 + (480216697/75675600)*n^2 + (6472/819)*n + 5 for n>7
%e Some solutions for n=4
%e ..1..2..2....0..0..1....0..1..2....0..1..2....1..2..2....0..0..0....0..0..1
%e ..2..2..1....0..1..3....0..2..4....1..3..3....2..2..1....0..1..2....0..1..2
%e ..3..2..1....1..3..4....2..2..2....2..3..4....3..3..3....1..2..3....1..2..1
%e ..4..4..3....3..3..2....4..2..0....3..2..3....4..4..4....2..2..2....3..2..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jun 25 2013