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%I #5 Mar 31 2012 12:37:16
%S 23,529,6819,100997,1482361,21553541,312522517,4536114221,65902168601,
%T 957521298093,13909906953981,202056095696637,2935122503702229,
%U 42637141306785073,619370827598445297,8997297666280027469
%N Number of nX3 0..2 arrays avoiding the patterns z z+1 z or z z-1 z in any row, column or nw-se diagonal
%C Column 3 of A207228
%H R. H. Hardin, <a href="/A207223/b207223.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 22*a(n-1) -189*a(n-2) +1291*a(n-3) -2505*a(n-4) +5630*a(n-5) +66182*a(n-6) +85302*a(n-7) -183268*a(n-8) +1122516*a(n-9) -9288376*a(n-10) -101606268*a(n-11) -163267092*a(n-12) +1028924256*a(n-13) +4615809720*a(n-14) +1632232760*a(n-15) -27698927152*a(n-16) -65399272512*a(n-17) -869805664*a(n-18) +215485870432*a(n-19) +387139064704*a(n-20) +292441453184*a(n-21) -149794976256*a(n-22) -937237304320*a(n-23) -2455615604224*a(n-24) -4166262247936*a(n-25) -3747983007744*a(n-26) +1241264136192*a(n-27) +10822269165568*a(n-28) +19311970320384*a(n-29) +22552503418880*a(n-30) +17593856000000*a(n-31) +10047152717824*a(n-32) +2601583640576*a(n-33) -536427364352*a(n-34) -1558695641088*a(n-35) -695902142464*a(n-36) -247765925888*a(n-37) +131667591168*a(n-38) +96770981888*a(n-39) +22817013760*a(n-40) +2147483648*a(n-41) -15032385536*a(n-42) +2147483648*a(n-43) for n>46
%e Some solutions for n=4
%e ..0..0..2....2..0..1....1..1..2....2..1..0....2..2..0....1..2..2....1..2..2
%e ..0..0..2....0..0..2....1..1..1....0..1..1....0..0..2....1..1..1....0..0..1
%e ..0..0..0....1..1..2....0..1..1....1..1..1....2..0..0....1..0..0....2..2..0
%e ..1..2..0....1..1..1....2..1..0....2..2..2....1..0..2....2..2..2....1..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Feb 16 2012
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