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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 23:22 EST 2021. Contains 349445 sequences. (Running on oeis4.)