A267719 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column greater than the previous repeated value.

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 12, 81, 102, 81, 12, 16, 144, 270, 270, 144, 16, 20, 256, 546, 872, 546, 256, 20, 25, 400, 1080, 1915, 1915, 1080, 400, 25, 30, 625, 1866, 4266, 4444, 4266, 1866, 625, 30, 36, 900, 3186, 7879, 10489, 10489, 7879, 3186, 900, 36, 42, 1296

Offset: 1

Author

R. H. Hardin, Jan 19 2016

Keywords

• nonn
• tabl

Comments

Table starts

..2....4....6.....9.....12.....16.....20......25......30.......36.......42

..4...16...36....81....144....256....400.....625.....900.....1296.....1764

..6...36..102...270....546...1080...1866....3186....5010.....7830....11550

..9...81..270...872...1915...4266...7879...14632...24440....40816....63714

.12..144..546..1915...4444..10489..20226...39485...68430...119560...192852

.16..256.1080..4266..10489..26906..54887..114392..209470...385962...656670

.20..400.1866..7879..20226..54887.116036..255009..481390...932245..1627470

.25..625.3186.14632..39485.114392.255009..592110.1179367..2391952..4403235

.30..900.5010.24440..68430.209470.481390.1179367.2411426..5148115..9689432

.36.1296.7830.40816.119560.385962.932245.2391952.5148115.11438402.22656990

Examples

			Some solutions for n=5 k=4
..1..0..0..1....0..1..1..0....1..1..0..1....0..1..1..0....1..0..0..1
..1..0..1..1....1..0..0..1....0..1..1..0....1..0..0..1....1..0..1..1
..0..1..0..0....0..1..1..0....1..0..1..1....0..0..1..0....0..1..0..0
..1..1..0..1....1..0..1..1....0..1..0..0....0..1..0..0....1..0..1..1
..0..0..1..0....1..1..0..1....1..0..1..0....1..1..0..1....0..1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..543

Crossrefs

Column 1 is A002620(n+2).

Column 2 is A030179(n+2).

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)

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)

k=3: [order 12]

k=4: [order 16] for n>18

k=5: [order 20] for n>22

k=6: [order 24] for n>27

k=7: [order 28] for n>30