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%I #4 Dec 30 2014 11:52:28
%S 121,377,1217,3787,11506,31999,86922,217799,537127,1242718,2846066,
%T 6208632,13461284,28145490,58668559,119104209,241640885,481269481,
%U 959688428,1890550722,3733605722,7319677531,14396259965,28207082638
%N Number of (3+1)X(n+1) 0..1 arrays with every 2X2 subblock sum nondecreasing horizontally, vertically and antidiagonally ne-to-sw
%C Row 3 of A253326
%H R. H. Hardin, <a href="/A253328/b253328.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +20*a(n-2) -98*a(n-3) -168*a(n-4) +1122*a(n-5) +674*a(n-6) -7970*a(n-7) -205*a(n-8) +39322*a(n-9) -13326*a(n-10) -142896*a(n-11) +86380*a(n-12) +395612*a(n-13) -325028*a(n-14) -850708*a(n-15) +867429*a(n-16) +1433880*a(n-17) -1752520*a(n-18) -1894178*a(n-19) +2759240*a(n-20) +1938970*a(n-21) -3430470*a(n-22) -1491450*a(n-23) +3380665*a(n-24) +795530*a(n-25) -2631230*a(n-26) -214060*a(n-27) +1599540*a(n-28) -65400*a(n-29) -744088*a(n-30) +104272*a(n-31) +255920*a(n-32) -56864*a(n-33) -61344*a(n-34) +17856*a(n-35) +9152*a(n-36) -3200*a(n-37) -640*a(n-38) +256*a(n-39)
%e Some solutions for n=4
%e ..0..0..0..1..1....0..1..1..1..1....0..1..0..1..1....0..0..0..0..1
%e ..0..1..0..0..0....0..1..0..1..0....0..0..0..0..0....0..0..0..0..0
%e ..1..0..1..1..1....1..1..1..1..1....1..0..1..1..1....1..0..1..1..1
%e ..0..1..0..1..1....1..0..1..0..1....0..1..0..1..1....0..0..1..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 30 2014
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