%I #4 Jun 30 2013 06:42:58
%S 20,124,643,2934,11810,42295,136553,402898,1099681,2805516,6748051,
%T 15412421,33626114,70430760,142218700,277853319,526833214,972034792,
%U 1749218167,3076360168,5297051430,8943742393,14828643583,24172697248
%N Number of nX3 -2..2 arrays of 2X2 subblock diagonal sums minus antidiagonal sums for some (n+1)X4 binary array with rows and columns of the latter in lexicographically nondecreasing order
%C Column 3 of A227060
%H R. H. Hardin, <a href="/A227057/b227057.txt">Table of n, a(n) for n = 1..39</a>
%F Empirical: a(n) = (1/1307674368000)*n^15 + (1/10897286400)*n^14 + (47/9340531200)*n^13 + (79/479001600)*n^12 + (25931/7185024000)*n^11 + (347/6220800)*n^10 + (143197/228614400)*n^9 + (1567309/304819200)*n^8 + (5780059/186624000)*n^7 + (244579/1741824)*n^6 + (370033369/718502400)*n^5 + (25976963/17107200)*n^4 + (4033604297/1135134000)*n^3 + (958946909/151351200)*n^2 + (55255/8008)*n + 1
%e Some solutions for n=3
%e ..0..1..0....0..0..0....0..1.-1....0..1.-2....0.-2..1....1..0..0....0..1.-1
%e ..1.-1..0....0..0..1....1.-1..0....1.-2..1....0..0..0...-2..1..0....1.-1.-1
%e .-2..1..0....0..1.-2...-1.-1..0...-1..0..0....0..0..0....0..0..0...-2..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_ Jun 30 2013