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A267667 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

%I A267667 #4 Jan 19 2016 08:08:39
%S A267667 1,2,2,3,8,4,5,18,32,7,7,50,108,98,12,11,98,500,453,288,20,15,242,
%T A267667 1372,3143,1800,800,33,23,450,5324,10933,18432,6654,2178,54,31,1058,
%U A267667 13500,60401,80404,98438,23967,5832,88,47,1922,48668,188301,624476,528980
%N A267667 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
%C A267667 Table starts
%C A267667 ...1.....2.......3........5.........7..........11...........15............23
%C A267667 ...2.....8......18.......50........98.........242..........450..........1058
%C A267667 ...4....32.....108......500......1372........5324........13500.........48668
%C A267667 ...7....98.....453.....3143.....10933.......60401.......188301........951113
%C A267667 ..12...288....1800....18432.....80404......624476......2369260......16599404
%C A267667 ..20...800....6654....98438....528980.....5663798.....25652956.....245171384
%C A267667 ..33..2178...23967...508681...3351233....49212395....264709135....3440837625
%C A267667 ..54..5832...84552..2560344..20607770...413258400...2629810220...46354321490
%C A267667 ..88.15488..295176.12721832.124968034..3417993766..25695609592..614111962042
%C A267667 .143.40898.1023321.62688891.751679881.28026084373.248940754959.8066250323665
%H A267667 R. H. Hardin, <a href="/A267667/b267667.txt">Table of n, a(n) for n = 1..179</a>
%F A267667 Empirical for column k:
%F A267667 k=1: a(n) = 2*a(n-1) -a(n-3)
%F A267667 k=2: a(n) = 4*a(n-1) -2*a(n-2) -6*a(n-3) +4*a(n-4) +2*a(n-5) -a(n-6)
%F A267667 k=3: [order 16]
%F A267667 k=4: [order 80]
%F A267667 Empirical for row n:
%F A267667 n=1: a(n) = a(n-1) +2*a(n-2) -2*a(n-3)
%F A267667 n=2: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -8*a(n-4) +8*a(n-5)
%F A267667 n=3: a(n) = a(n-1) +14*a(n-2) -14*a(n-3) -56*a(n-4) +56*a(n-5) +64*a(n-6) -64*a(n-7)
%F A267667 n=4: [order 21]
%F A267667 n=5: [order 96]
%e A267667 Some solutions for n=5 k=4
%e A267667 ..0..1..0..1....0..1..1..0....0..0..1..0....0..1..0..1....0..1..1..0
%e A267667 ..0..0..1..1....0..0..1..1....1..0..1..1....1..1..0..0....0..0..1..1
%e A267667 ..1..1..0..0....0..0..1..1....0..1..1..0....0..0..1..1....1..0..1..0
%e A267667 ..0..1..0..1....1..0..0..1....1..0..0..1....0..1..0..0....0..0..1..0
%e A267667 ..0..1..0..1....0..0..1..1....1..0..1..0....0..0..1..1....0..1..0..1
%Y A267667 Column 1 is A000071(n+2).
%Y A267667 Row 1 is A052955(n-1).
%Y A267667 Row 2 is A267638.
%K A267667 nonn,tabl
%O A267667 1,2
%A A267667 _R. H. Hardin_, Jan 19 2016