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%I #5 Mar 31 2012 12:37:13
%S 25,625,11092,192575,3425501,61164640,1090023439,19411973287,
%T 345764258689,6159551322461,109726321617078,1954613166621694,
%U 34818594738203574,620246036769753113,11048844392776786913
%N Number of nX3 0..2 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal
%C Column 3 of A206863
%H R. H. Hardin, <a href="/A206858/b206858.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 19*a(n-1) -116*a(n-2) +1656*a(n-3) -869*a(n-4) +21477*a(n-5) +132055*a(n-6) -840588*a(n-7) +536035*a(n-8) -6853600*a(n-9) -60451483*a(n-10) +239622640*a(n-11) +438741327*a(n-12) -1195377988*a(n-13) +5700951257*a(n-14) -6858573805*a(n-15) -111005025152*a(n-16) +81130949991*a(n-17) +729595094458*a(n-18) -164145675576*a(n-19) -1939309566165*a(n-20) -923748685709*a(n-21) -1316253867500*a(n-22) +5260520510689*a(n-23) +20022040020338*a(n-24) -5890585307291*a(n-25) -34836595129811*a(n-26) -22702031279219*a(n-27) -33049844533404*a(n-28) +62351641745134*a(n-29) +155113662891657*a(n-30) +33107662721068*a(n-31) -24178641337873*a(n-32) -194402042599881*a(n-33) -311832321249112*a(n-34) -33618123825367*a(n-35) +89850785718241*a(n-36) +300778171884747*a(n-37) +374045469527943*a(n-38) +86092340636653*a(n-39) +3604652678449*a(n-40) -201637013534345*a(n-41) -207248865450281*a(n-42) -71047680122596*a(n-43) -57323557161104*a(n-44) +59400218029312*a(n-45) +25376225539103*a(n-46) +1328368282685*a(n-47) +4014897641042*a(n-48) -31160253752859*a(n-49) +1838520623206*a(n-50) -6407828259429*a(n-51) +3995902092267*a(n-52) +3720821190410*a(n-53) -1212803780265*a(n-54) +697965261753*a(n-55) -2333237925074*a(n-56) -547181285476*a(n-57) -915715203554*a(n-58) -261550523386*a(n-59) -181827672515*a(n-60) -54985098044*a(n-61) -21779928260*a(n-62) -6733838628*a(n-63) -1623288484*a(n-64) -490248576*a(n-65) -68943120*a(n-66) -19647216*a(n-67) -1205568*a(n-68) -323136*a(n-69)
%e Some solutions for n=4
%e ..0..1..2....2..0..1....0..0..2....2..1..0....2..1..2....2..2..1....2..0..2
%e ..1..2..0....0..0..2....0..0..2....0..1..1....1..2..2....2..0..2....1..1..1
%e ..1..2..0....1..1..2....0..0..0....1..0..2....0..2..1....2..2..0....1..1..0
%e ..2..0..2....1..1..1....1..2..0....1..2..2....1..1..2....0..2..1....1..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Feb 13 2012
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