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%I #4 Jan 12 2014 07:10:23
%S 144,1120,8046,53728,336836,2000524,11372978,62383454,332455972,
%T 1730326282,8833514496,44382185226,220072436430,1079376436068,
%U 5246129716196,25306054280836,121306074550810,578457574821664
%N Number of (n+1)X(3+1) 0..1 arrays with the difference of the upper and lower median value of each 2X2 subblock in lexicographically nondecreasing order rowwise and columnwise
%C Column 3 of A235573
%H R. H. Hardin, <a href="/A235568/b235568.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) -9*a(n-2) -541*a(n-3) +1696*a(n-4) +9722*a(n-5) -46888*a(n-6) -95212*a(n-7) +697497*a(n-8) +481891*a(n-9) -6809749*a(n-10) -30189*a(n-11) +47373245*a(n-12) -19406431*a(n-13) -245219703*a(n-14) +167953633*a(n-15) +968126450*a(n-16) -852757916*a(n-17) -2955610502*a(n-18) +3039768838*a(n-19) +7021153815*a(n-20) -8047471703*a(n-21) -12981161773*a(n-22) +16175042271*a(n-23) +18580676002*a(n-24) -24843301208*a(n-25) -20361671632*a(n-26) +29053537392*a(n-27) +16774827040*a(n-28) -25551955968*a(n-29) -10103359744*a(n-30) +16522906624*a(n-31) +4261513216*a(n-32) -7569866752*a(n-33) -1174028288*a(n-34) +2308964352*a(n-35) +186122240*a(n-36) -417333248*a(n-37) -12582912*a(n-38) +33554432*a(n-39)
%e Some solutions for n=4
%e ..0..0..1..0....0..1..0..1....0..0..0..0....1..0..0..1....0..1..1..0
%e ..0..1..1..0....0..0..0..1....1..0..0..0....0..0..0..0....0..0..1..0
%e ..1..1..0..1....1..0..0..1....0..0..0..0....0..0..0..0....0..0..0..1
%e ..1..1..0..0....0..0..0..1....1..0..0..0....1..0..1..0....0..0..1..0
%e ..0..0..1..0....0..1..0..1....0..0..0..1....0..0..1..0....1..0..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2014
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