%I #5 Mar 31 2012 12:37:02
%S 699151,3418839,18296109,306913392,3151347159,29239334379,
%T 379274173335,3641409829935,34620279251220,418417981047306,
%U 4096732979422647,40558686661842885,466567312647906171,4645894923118379898
%N Number of (n+2)X5 0..2 arrays with every 3X3 subblock having three strictly increasing elements in a row horizontally or vertically
%C Column 3 of A204501
%H R. H. Hardin, <a href="/A204496/b204496.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 1459*a(n-3) +2005*a(n-4) +5310*a(n-5) -511983*a(n-6) -1249810*a(n-7) -1338909*a(n-8) +777384*a(n-9) +63820566*a(n-10) -147709668*a(n-11) +238990122*a(n-12) -916135317*a(n-13) -4608149598*a(n-14) -3940949205*a(n-15) +7990407837*a(n-16) +220252549014*a(n-17) +676649077299*a(n-18) -164172129993*a(n-19) -571730300937*a(n-20) -9237319418664*a(n-21) -20628023965983*a(n-22) -11834560642464*a(n-23) +17255332260783*a(n-24) +161544104529498*a(n-25) +47857887606762*a(n-26) +625306625984133*a(n-27) -1730900000913021*a(n-28) +304887438662949*a(n-29) -1164464483337036*a(n-30) -4124479186986921*a(n-31) +9929079530820522*a(n-32) -2586980066588397*a(n-33) -9923892788872269*a(n-34) +17371684565907696*a(n-35) -9285100480065060*a(n-36) +13522081539016584*a(n-37) -2122141045534452*a(n-38) +989039140361712*a(n-39) +46907074411776*a(n-40) +1961780498797392*a(n-41) +51490536208848*a(n-42) +93063567064320*a(n-43) -53061110173440*a(n-44) -1101996057600*a(n-46) for n>50
%e Some solutions for n=3
%e ..1..1..0..1..1....0..2..0..0..1....1..0..1..1..2....0..0..0..0..1
%e ..1..2..1..0..2....1..1..2..1..0....0..1..0..1..1....2..0..0..1..1
%e ..1..0..2..1..2....2..0..1..2..1....1..2..0..1..2....0..1..2..2..1
%e ..0..1..2..2..2....0..1..2..2..2....2..0..1..2..0....0..2..0..1..2
%e ..0..2..0..1..2....0..0..0..1..2....2..1..2..2..0....0..0..1..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 15 2012