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%I #4 Jan 15 2014 10:05:18
%S 120,628,2994,12417,47501,166904,552444,1724793,5144350,14696712,
%T 40503441,107993795,279771656,706134649,1741178487,4204576953,
%U 9961571579,23204492256,53213406141,120352868718,268716844980,593201019964
%N Number of (n+1)X(3+1) 0..1 arrays with the sum of each 2X2 subblock two extreme terms minus its two median terms lexicographically nondecreasing columnwise and nonincreasing rowwise
%C Column 3 of A235772
%H R. H. Hardin, <a href="/A235768/b235768.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +22*a(n-2) -106*a(n-3) -206*a(n-4) +1310*a(n-5) +970*a(n-6) -10018*a(n-7) -1220*a(n-8) +53030*a(n-9) -14210*a(n-10) -205870*a(n-11) +113050*a(n-12) +605570*a(n-13) -469970*a(n-14) -1374070*a(n-15) +1346965*a(n-16) +2422430*a(n-17) -2874380*a(n-18) -3308560*a(n-19) +4711492*a(n-20) +3445592*a(n-21) -6005504*a(n-22) -2628928*a(n-23) +5959072*a(n-24) +1319360*a(n-25) -4565120*a(n-26) -254464*a(n-27) +2650240*a(n-28) -198400*a(n-29) -1127936*a(n-30) +203264*a(n-31) +332032*a(n-32) -88576*a(n-33) -60416*a(n-34) +20480*a(n-35) +5120*a(n-36) -2048*a(n-37)
%e Some solutions for n=4
%e ..1..0..0..1....1..0..0..0....1..0..0..1....1..1..0..1....0..1..0..0
%e ..0..1..0..0....1..0..1..0....1..0..0..0....1..1..0..0....1..0..1..0
%e ..0..1..0..1....1..0..1..0....1..0..0..0....1..0..1..0....0..1..0..0
%e ..0..1..1..0....1..1..0..0....1..1..1..0....1..1..1..0....1..1..1..1
%e ..1..0..1..1....1..0..1..1....1..0..0..0....0..1..0..1....0..1..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 15 2014
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