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A267788 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.

%I A267788 #4 Jan 20 2016 12:31:18
%S A267788 2,4,4,8,16,6,15,64,36,9,28,225,216,81,12,51,784,1056,729,144,16,92,
%T A267788 2601,5004,5081,1728,256,20,164,8464,22110,34173,14956,4096,400,25,
%U A267788 290,26896,94554,211555,122770,44742,8000,625,30,509,84100,391314,1262760,912667
%N A267788 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.
%C A267788 Table starts
%C A267788 ..2....4.....8.....15.......28........51.........92.........164..........290
%C A267788 ..4...16....64....225......784......2601.......8464.......26896........84100
%C A267788 ..6...36...216...1056.....5004.....22110......94554......391314......1582824
%C A267788 ..9...81...729...5081....34173....211555....1262760.....7263481.....40755550
%C A267788 .12..144..1728..14956...122770....912667....6484282....44116906....291598056
%C A267788 .16..256..4096..44742...460598...4245574...37282358...312449872...2540944329
%C A267788 .20..400..8000.102954..1234716..13126812..132388406..1271314080..11831791048
%C A267788 .25..625.15625.238813..3380133..42012357..494152778..5520112546..59723941668
%C A267788 .30..900.27000.472174..7591852.106570618.1413416776.17806098826.217360101006
%C A267788 .36.1296.46656.935890.17155354.272337497.4075463059.57801662876.793861159136
%H A267788 R. H. Hardin, <a href="/A267788/b267788.txt">Table of n, a(n) for n = 1..200</a>
%F A267788 Empirical for column k:
%F A267788 k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
%F A267788 k=2: a(n) = 2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8)
%F A267788 k=3: [order 12]
%F A267788 k=4: [order 16] for n>18
%F A267788 k=5: [order 20] for n>22
%F A267788 k=6: [order 24] for n>27
%F A267788 Empirical for row n:
%F A267788 n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A267788 n=2: [order 9]
%F A267788 n=3: [order 12]
%F A267788 n=4: [order 93]
%e A267788 Some solutions for n=4 k=4
%e A267788 ..1..0..1..0....1..0..0..0....0..1..0..0....1..1..1..0....1..1..0..1
%e A267788 ..0..1..0..1....1..1..0..1....0..0..0..0....0..0..0..0....0..0..0..0
%e A267788 ..0..0..1..0....0..0..1..1....1..1..1..1....0..1..0..1....1..1..1..1
%e A267788 ..1..1..1..1....1..0..0..0....1..0..1..0....1..1..1..1....1..0..0..0
%Y A267788 Column 1 is A002620(n+2).
%Y A267788 Column 2 is A030179(n+2).
%Y A267788 Row 1 is A029907(n+1).
%Y A267788 Row 2 is A267729.
%K A267788 nonn,tabl
%O A267788 1,1
%A A267788 _R. H. Hardin_, Jan 20 2016