A267638 -id:A267638 - cp's OEIS frontend

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

R. H. Hardin, Jan 19 2016

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

			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

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

Column 1 is A000071(n+2).
Row 1 is A052955(n-1).
Row 2 is A267638.

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]

cp's OEIS Frontend

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.

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