A267644 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 2, 3, 8, 3, 5, 18, 18, 5, 7, 50, 51, 50, 7, 11, 98, 189, 189, 98, 11, 15, 242, 429, 1015, 429, 242, 15, 23, 450, 1353, 2887, 2887, 1353, 450, 23, 31, 1058, 2829, 12623, 8917, 12623, 2829, 1058, 31, 47, 1922, 8427, 32303, 47715, 47715, 32303, 8427, 1922, 47, 63

Offset: 1

Author

R. H. Hardin, Jan 18 2016

Keywords

• nonn
• tabl

Comments

Table starts

..1....2.....3.......5.......7........11........15..........23..........31

..2....8....18......50......98.......242.......450........1058........1922

..3...18....51.....189.....429......1353......2829........8427.......16899

..5...50...189....1015....2887.....12623.....32303......131673......319541

..7...98...429....2887....8917.....47715....128441......647101.....1614281

.11..242..1353...12623...47715....343145...1117207.....7479533....22499181

.15..450..2829...32303..128441...1117207...3696933....30649693....90914453

.23.1058..8427..131673..647101...7479533..30649693...330654951..1225925501

.31.1922.16899..319541.1614281..22499181..90914453..1225925501..4301737251

.47.4418.49443.1277029.8168679.150415627.784186403.13431652713.62439362175

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A052955(n-1).

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -8*a(n-4) +8*a(n-5)

k=3: [order 11]

k=4: [order 35]

k=5: [order 93]