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%I #5 Mar 31 2012 12:37:16
%S 25,625,12534,247163,4916282,97935886,1950327875,38835489653,
%T 773312516026,15398704815066,306628906800995,6105789048401634,
%U 121582346211823189,2421024919176322257,48208985952384503326
%N Number of nX3 0..2 arrays avoiding the pattern z z+1 z in any row or column
%C Column 3 of A207221
%H R. H. Hardin, <a href="/A207216/b207216.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 19*a(n-1) -80*a(n-2) +1817*a(n-3) +393*a(n-4) +40639*a(n-5) +135655*a(n-6) -288018*a(n-7) +1383524*a(n-8) -6460141*a(n-9) -42527369*a(n-10) +54473671*a(n-11) -3651045*a(n-12) -176749122*a(n-13) +4407855135*a(n-14) +2709812836*a(n-15) -34919565552*a(n-16) -27447585535*a(n-17) +113274818974*a(n-18) +114838914140*a(n-19) -128539719662*a(n-20) -192736763296*a(n-21) -152774223996*a(n-22) -36302533050*a(n-23) +472340733412*a(n-24) +502775352861*a(n-25) -65829409260*a(n-26) -326138062718*a(n-27) -608987401872*a(n-28) -496677891503*a(n-29) +211702810836*a(n-30) +457318062888*a(n-31) +468410661487*a(n-32) +313611961167*a(n-33) -126649818836*a(n-34) -268635687911*a(n-35) -246107284607*a(n-36) -166980560951*a(n-37) +4064457411*a(n-38) +64871730646*a(n-39) +73590617020*a(n-40) +58177206255*a(n-41) +18030791535*a(n-42) +865842795*a(n-43) -7967186465*a(n-44) -8986570910*a(n-45) -4749899549*a(n-46) -2540040800*a(n-47) -578469622*a(n-48) +169446405*a(n-49) +199570174*a(n-50) +252247666*a(n-51) +91768452*a(n-52) +69302160*a(n-53) +17497762*a(n-54) +10560678*a(n-55) +1955316*a(n-56) +1012729*a(n-57) +133774*a(n-58) +61516*a(n-59) +5238*a(n-60) +2199*a(n-61) +90*a(n-62) +36*a(n-63)
%e Some solutions for n=4
%e ..2..1..2....2..1..0....2..0..1....1..0..1....2..2..0....0..1..2....1..1..2
%e ..1..2..2....0..1..1....0..0..2....2..0..2....0..0..2....1..2..0....1..1..1
%e ..0..2..1....1..0..2....1..1..2....0..2..2....2..0..0....1..2..0....0..1..2
%e ..1..1..2....1..2..2....1..1..1....2..0..2....1..0..1....2..0..1....2..1..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Feb 16 2012
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