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%I #4 Jan 12 2014 06:02:39
%S 120,814,5567,33851,184281,892122,3925717,15834473,59506551,209811804,
%T 701617754,2235893345,6840089137,20153696074,57486754527,159114503083,
%U 428959896263,1128320167213,2903976632760,7322640491124,18130800682746
%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 rowwise and columnwise
%C Column 3 of A235555
%H R. H. Hardin, <a href="/A235551/b235551.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +35*a(n-2) -158*a(n-3) -566*a(n-4) +2984*a(n-5) +5518*a(n-6) -35860*a(n-7) -34899*a(n-8) +307860*a(n-9) +134985*a(n-10) -2009442*a(n-11) -146036*a(n-12) +10361384*a(n-13) -2055944*a(n-14) -43291072*a(n-15) +17856377*a(n-16) +149141740*a(n-17) -88146091*a(n-18) -428837090*a(n-19) +320702778*a(n-20) +1037666520*a(n-21) -926474634*a(n-22) -2123839620*a(n-23) +2196630507*a(n-24) +3685625340*a(n-25) -4350171921*a(n-26) -5420700030*a(n-27) +7267723728*a(n-28) +6732949080*a(n-29) -10298203356*a(n-30) -7007379432*a(n-31) +12402868752*a(n-32) +6021828864*a(n-33) -12690037008*a(n-34) -4154733792*a(n-35) +10997624704*a(n-36) +2163244160*a(n-37) -8028312512*a(n-38) -698220160*a(n-39) +4894723328*a(n-40) -31167488*a(n-41) -2461727488*a(n-42) +213300736*a(n-43) +1003462656*a(n-44) -156899328*a(n-45) -323171328*a(n-46) +70256640*a(n-47) +79130624*a(n-48) -21463040*a(n-49) -13840384*a(n-50) +4415488*a(n-51) +1540096*a(n-52) -557056*a(n-53) -81920*a(n-54) +32768*a(n-55)
%e Some solutions for n=5
%e ..0..1..0..0....0..1..1..1....1..0..1..1....0..1..1..1....1..0..1..0
%e ..1..1..1..1....1..1..1..1....1..1..1..1....1..1..0..1....1..1..0..1
%e ..0..1..1..0....0..1..1..1....0..1..1..0....1..1..0..1....0..1..0..0
%e ..1..0..1..0....1..1..1..1....1..0..0..1....1..1..0..1....1..0..1..0
%e ..0..1..1..0....1..1..0..0....0..1..0..1....0..0..1..0....0..0..1..0
%e ..0..0..0..0....1..1..1..0....0..0..0..0....0..0..1..0....1..0..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2014
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