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%I #4 Mar 02 2014 09:18:22
%S 1,2,2,3,8,3,5,18,18,5,8,50,51,50,8,13,128,189,189,128,13,21,338,630,
%T 1015,630,338,21,34,882,2187,4742,4742,2187,882,34,55,2312,7473,23373,
%U 30116,23373,7473,2312,55,89,6050,25692,112827,204216,204216,112827
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..1 introduced in row major order
%C Table starts
%C ..1.....2......3........5.........8..........13...........21.............34
%C ..2.....8.....18.......50.......128.........338..........882...........2312
%C ..3....18.....51......189.......630........2187.........7473..........25692
%C ..5....50....189.....1015......4742.......23373.......112827.........549068
%C ..8...128....630.....4742.....30116......204216......1349732........9010526
%C .13...338...2187....23373....204216.....1929041.....17672899......163862944
%C .21...882...7473...112827...1349732....17672899....223336353.....2861990416
%C .34..2312..25692...549068...9010526...163862944...2861990416....50789138692
%C .55..6050..88119..2663629..59917746..1512215465..36475373351...895686099682
%C .89.15842.302511.12937577.399048464.13981375097.465876675157.15835026599714
%H R. H. Hardin, <a href="/A238654/b238654.txt">Table of n, a(n) for n = 1..287</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
%F k=3: a(n) = 2*a(n-1) +5*a(n-2) -a(n-4)
%F k=4: [order 20]
%F k=5: [order 68]
%e Some solutions for n=5 k=4
%e ..0..1..0..0..1..0....0..1..0..0..1..0....0..1..0..1..0..1....0..1..0..1..1..0
%e ..1..0..1..1..0..1....1..0..1..1..0..1....1..0..1..0..1..0....1..0..1..0..0..1
%e ..0..1..0..0..1..0....0..1..0..1..0..1....0..1..0..1..0..1....0..1..0..1..1..0
%e ..0..1..1..0..0..1....0..1..0..0..1..0....0..1..0..0..1..0....1..0..0..1..0..1
%e ..1..0..0..1..1..0....1..0..1..1..0..1....1..0..1..0..0..1....1..0..1..0..1..0
%e ..1..0..1..0..0..1....1..0..1..0..0..1....1..0..1..1..0..1....0..1..0..0..1..0
%e ..0..1..0..1..1..0....0..1..0..1..1..0....0..1..0..0..1..0....1..0..1..1..0..1
%Y Column 1 is A000045(n+1)
%Y Column 2 is A175395(n+1)
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 02 2014
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