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%I #4 Dec 30 2014 11:53:06
%S 286,848,2538,7744,23153,66196,185672,487946,1267072,3085862,7470280,
%T 17091282,39029883,84989350,185271083,388424614,817078868,1665997116,
%U 3414304408,6830298216,13751307597,27192582550,54155269965,106492298012
%N Number of (4+1)X(n+1) 0..1 arrays with every 2X2 subblock sum nondecreasing horizontally, vertically and antidiagonally ne-to-sw
%C Row 4 of A253326
%H R. H. Hardin, <a href="/A253329/b253329.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) -210*a(n-4) +1326*a(n-5) +1050*a(n-6) -10410*a(n-7) -1890*a(n-8) +57510*a(n-9) -11550*a(n-10) -237570*a(n-11) +112490*a(n-12) +760990*a(n-13) -524030*a(n-14) -1933810*a(n-15) +1690860*a(n-16) +3953670*a(n-17) -4149530*a(n-18) -6551950*a(n-19) +8061326*a(n-20) +8813506*a(n-21) -12654642*a(n-22) -9571614*a(n-23) +16226210*a(n-24) +8262514*a(n-25) -17073770*a(n-26) -5469910*a(n-27) +14742030*a(n-28) +2528970*a(n-29) -10398698*a(n-30) -534118*a(n-31) +5937701*a(n-32) -282818*a(n-33) -2703540*a(n-34) +352848*a(n-35) +958860*a(n-36) -192600*a(n-37) -255360*a(n-38) +66720*a(n-39) +48048*a(n-40) -15072*a(n-41) -5696*a(n-42) +2048*a(n-43) +320*a(n-44) -128*a(n-45)
%e Some solutions for n=4
%e ..0..0..0..1..0....1..0..1..0..1....0..0..0..1..1....0..0..0..1..1
%e ..1..0..1..0..1....0..0..0..0..0....0..0..0..1..0....1..0..1..0..0
%e ..0..1..0..1..0....1..0..1..0..1....1..1..1..1..1....0..1..0..1..1
%e ..1..1..1..1..1....0..0..1..0..1....0..1..0..1..0....1..0..1..1..1
%e ..0..1..0..1..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 30 2014
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