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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A052955(n-1).

Sequence in context: A177696 A134574 A141617 * A204197 A238654 A220553

Adjacent sequences: A267641 A267642 A267643 * A267645 A267646 A267647

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 18 2016

Status

approved