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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. 13
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 19 2016
STATUS
approved

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Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)