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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A002620(n+2).

Column 2 is A030179(n+2).

Sequence in context: A209650 A207599 A207703 * A207752 A207514 A207879

Adjacent sequences: A267716 A267717 A267718 * A267720 A267721 A267722

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 19 2016

Status

approved