A267667 T(n,k)=Number of nXk 0..1 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

1, 2, 2, 3, 8, 4, 5, 18, 32, 7, 7, 50, 108, 98, 12, 11, 98, 500, 453, 288, 20, 15, 242, 1372, 3143, 1800, 800, 33, 23, 450, 5324, 10933, 18432, 6654, 2178, 54, 31, 1058, 13500, 60401, 80404, 98438, 23967, 5832, 88, 47, 1922, 48668, 188301, 624476, 528980

Offset

1,2

Comments

Table starts

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

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

...4....32.....108......500......1372........5324........13500.........48668

...7....98.....453.....3143.....10933.......60401.......188301........951113

..12...288....1800....18432.....80404......624476......2369260......16599404

..20...800....6654....98438....528980.....5663798.....25652956.....245171384

..33..2178...23967...508681...3351233....49212395....264709135....3440837625

..54..5832...84552..2560344..20607770...413258400...2629810220...46354321490

..88.15488..295176.12721832.124968034..3417993766..25695609592..614111962042

.143.40898.1023321.62688891.751679881.28026084373.248940754959.8066250323665

Links

R. H. Hardin, Table of n, a(n) for n = 1..179

Formula

Empirical for column k:

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

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

k=3: [order 16]

k=4: [order 80]

Empirical for row n:

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

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

n=3: a(n) = a(n-1) +14*a(n-2) -14*a(n-3) -56*a(n-4) +56*a(n-5) +64*a(n-6) -64*a(n-7)

n=4: [order 21]

n=5: [order 96]

Example

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

Crossrefs

Column 1 is A000071(n+2).

Row 1 is A052955(n-1).

Row 2 is A267638.

Sequence in context: A220553 A176383 A100551 * A210190 A070267 A205374

Adjacent sequences: A267664 A267665 A267666 * A267668 A267669 A267670

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 19 2016

Status

approved