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%I #4 Dec 30 2014 08:25:38
%S 3550,10064,64560,266074,1547188,8858020,51974842,316785048,
%T 1889816848,11520937494,69228976028,420338522082,2533933878238,
%U 15348106027014,92666482760148,560658619860350,3387466997245654,20485364481865874
%N Number of (n+1)X(3+1) 0..2 arrays with every 2X2 subblock diagonal maximum minus antidiagonal maximum unequal to its neighbors horizontally, vertically, diagonally and antidiagonally
%C Column 3 of A253314
%H R. H. Hardin, <a href="/A253309/b253309.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) +37*a(n-2) -107*a(n-3) -486*a(n-4) +1018*a(n-5) +3866*a(n-6) -6206*a(n-7) -30268*a(n-8) +50703*a(n-9) +221999*a(n-10) -375260*a(n-11) -1183609*a(n-12) +1552867*a(n-13) +4427784*a(n-14) -4937769*a(n-15) -10826500*a(n-16) +22562360*a(n-17) +26189180*a(n-18) -87151773*a(n-19) -72448042*a(n-20) +306943717*a(n-21) +47064799*a(n-22) -1009281939*a(n-23) +378072841*a(n-24) +2761001674*a(n-25) -49050560*a(n-26) -6740013051*a(n-27) -3824848899*a(n-28) +13172695757*a(n-29) +14866122455*a(n-30) -24287462053*a(n-31) -32467094345*a(n-32) +73114969076*a(n-33) +67761287326*a(n-34) -151086224293*a(n-35) -163493264976*a(n-36) +141458795648*a(n-37) +256000189920*a(n-38) -28921058738*a(n-39) -179496036973*a(n-40) -27002949460*a(n-41) +34741117668*a(n-42) +862760100*a(n-43) -96042640*a(n-44) -2512546848*a(n-45) +556658720*a(n-46) +192661632*a(n-47) -84460160*a(n-48) +8505600*a(n-49) for n>55
%e Some solutions for n=3
%e ..0..0..0..0....0..1..2..0....2..1..0..2....1..0..1..2....1..1..1..0
%e ..0..0..2..1....0..1..0..2....0..2..0..2....0..2..0..2....2..0..2..0
%e ..1..2..0..0....2..0..0..0....1..0..0..0....1..1..0..1....0..0..0..1
%e ..1..0..1..1....2..0..2..1....2..1..2..2....0..0..2..0....2..2..1..2
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 30 2014
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