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%I #4 Jan 19 2016 20:17:14
%S 2,4,4,6,16,6,9,36,36,9,12,81,102,81,12,16,144,270,270,144,16,20,256,
%T 546,872,546,256,20,25,400,1080,1915,1915,1080,400,25,30,625,1866,
%U 4266,4444,4266,1866,625,30,36,900,3186,7879,10489,10489,7879,3186,900,36,42,1296
%N T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column greater than the previous repeated value.
%C Table starts
%C ..2....4....6.....9.....12.....16.....20......25......30.......36.......42
%C ..4...16...36....81....144....256....400.....625.....900.....1296.....1764
%C ..6...36..102...270....546...1080...1866....3186....5010.....7830....11550
%C ..9...81..270...872...1915...4266...7879...14632...24440....40816....63714
%C .12..144..546..1915...4444..10489..20226...39485...68430...119560...192852
%C .16..256.1080..4266..10489..26906..54887..114392..209470...385962...656670
%C .20..400.1866..7879..20226..54887.116036..255009..481390...932245..1627470
%C .25..625.3186.14632..39485.114392.255009..592110.1179367..2391952..4403235
%C .30..900.5010.24440..68430.209470.481390.1179367.2411426..5148115..9689432
%C .36.1296.7830.40816.119560.385962.932245.2391952.5148115.11438402.22656990
%H R. H. Hardin, <a href="/A267719/b267719.txt">Table of n, a(n) for n = 1..543</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
%F 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 k=3: [order 12]
%F k=4: [order 16] for n>18
%F k=5: [order 20] for n>22
%F k=6: [order 24] for n>27
%F k=7: [order 28] for n>30
%e Some solutions for n=5 k=4
%e ..1..0..0..1....0..1..1..0....1..1..0..1....0..1..1..0....1..0..0..1
%e ..1..0..1..1....1..0..0..1....0..1..1..0....1..0..0..1....1..0..1..1
%e ..0..1..0..0....0..1..1..0....1..0..1..1....0..0..1..0....0..1..0..0
%e ..1..1..0..1....1..0..1..1....0..1..0..0....0..1..0..0....1..0..1..1
%e ..0..0..1..0....1..1..0..1....1..0..1..0....1..1..0..1....0..1..0..0
%Y Column 1 is A002620(n+2).
%Y Column 2 is A030179(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 19 2016
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