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%I #5 Mar 31 2012 12:37:04
%S 1328,13116,171790,2323490,33432873,473468278,6825854177,97434972458,
%T 1400397520634,20040440280986,287600358488383,4119875835641658,
%U 59086396068054719,846765767843984246,12140883557782262680
%N Number of (n+1)X3 0..3 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock equal to the number in all its horizontal and vertical neighbors
%C Column 2 of A205097
%H R. H. Hardin, <a href="/A205091/b205091.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) +61*a(n-2) -1080*a(n-3) +4316*a(n-4) -2492*a(n-5) -64039*a(n-6) +381996*a(n-7) -1283276*a(n-8) +2785276*a(n-9) -1539170*a(n-10) -20283712*a(n-11) +116603963*a(n-12) -408274230*a(n-13) +1152730179*a(n-14) -2854787638*a(n-15) +6272522589*a(n-16) -12271092056*a(n-17) +21605332496*a(n-18) -34363071774*a(n-19) +49501258815*a(n-20) -65887238402*a(n-21) +84449247026*a(n-22) -111175677802*a(n-23) +160721683875*a(n-24) -249770812048*a(n-25) +374457895469*a(n-26) -501256989846*a(n-27) +591574369110*a(n-28) -619405129694*a(n-29) +560138970161*a(n-30) -404813416964*a(n-31) +205012837895*a(n-32) -55446182144*a(n-33) +3308435675*a(n-34) -9914554906*a(n-35) +15674895699*a(n-36) -4919460556*a(n-37) -5275625484*a(n-38) +4888957634*a(n-39) +255044772*a(n-40) -2974480434*a(n-41) +2609856714*a(n-42) -1564758900*a(n-43) +1031837204*a(n-44) -744099464*a(n-45) +375794957*a(n-46) -33609742*a(n-47) -115721758*a(n-48) +101669692*a(n-49) -44336021*a(n-50) +9842494*a(n-51) +120845*a(n-52) -802982*a(n-53) +252792*a(n-54) -37408*a(n-55) +2304*a(n-56) for n>60
%e Some solutions for n=4
%e ..1..2..0....0..3..2....1..1..1....3..2..1....1..0..0....3..2..1....2..1..3
%e ..3..0..1....2..1..3....2..0..1....1..0..0....0..0..0....1..2..2....0..1..1
%e ..0..1..0....1..2..0....3..0..0....0..0..0....0..0..0....1..0..2....0..0..1
%e ..1..1..2....2..0..3....1..1..0....0..0..0....0..0..0....2..0..0....1..0..0
%e ..0..2..0....3..1..1....2..1..1....0..0..0....0..0..0....1..1..0....1..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 22 2012
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