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%I #4 Jan 11 2014 13:24:09
%S 209,2501,29533,343063,3977050,45985647,531586422,6142770286,
%T 70981491138,820170288679,9476823620961,109501139670236,
%U 1265245059604933,14619424266289557,168921893229610261,1951828059463346253
%N Number of (n+1)X(3+1) 0..1 arrays with the sum of each 2X2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise
%C Column 3 of A235517
%H R. H. Hardin, <a href="/A235512/b235512.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 18*a(n-1) -35*a(n-2) -800*a(n-3) +3598*a(n-4) +11518*a(n-5) -86177*a(n-6) -43426*a(n-7) +1030208*a(n-8) -551932*a(n-9) -7523343*a(n-10) +8359408*a(n-11) +36977209*a(n-12) -55765580*a(n-13) -129333424*a(n-14) +236161174*a(n-15) +333558074*a(n-16) -701926806*a(n-17) -650276140*a(n-18) +1531081970*a(n-19) +977200374*a(n-20) -2507610186*a(n-21) -1152187728*a(n-22) +3118788662*a(n-23) +1084336743*a(n-24) -2956454312*a(n-25) -826149717*a(n-26) +2130992178*a(n-27) +511775800*a(n-28) -1158609216*a(n-29) -254345475*a(n-30) +468586344*a(n-31) +98077210*a(n-32) -138111794*a(n-33) -27921777*a(n-34) +28847250*a(n-35) +5513265*a(n-36) -4114646*a(n-37) -697128*a(n-38) +380368*a(n-39) +50000*a(n-40) -20704*a(n-41) -1536*a(n-42) +512*a(n-43)
%e Some solutions for n=3
%e ..0..0..1..1....1..0..0..1....1..0..1..0....1..0..1..1....1..1..1..0
%e ..1..1..1..0....0..0..1..0....0..0..1..0....1..0..0..0....1..0..1..0
%e ..1..0..1..0....1..0..1..1....0..1..0..1....1..0..1..0....0..1..1..0
%e ..0..1..0..1....1..1..0..0....0..1..0..1....0..1..1..1....0..0..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 11 2014
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