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A303636
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
7
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 3, 1, 1, 3, 0, 0, 5, 0, 4, 0, 5, 0, 0, 8, 3, 8, 8, 3, 8, 0, 0, 13, 2, 22, 20, 22, 2, 13, 0, 0, 21, 9, 47, 66, 66, 47, 9, 21, 0, 0, 34, 12, 123, 207, 394, 207, 123, 12, 34, 0, 0, 55, 33, 302, 726, 1417, 1417, 726, 302, 33, 55, 0, 0, 89, 56, 784
OFFSET
1,12
COMMENTS
Table starts
.0..0..0...0....0.....0......0.......0........0.........0..........0
.0..1..1...2....3.....5......8......13.......21........34.........55
.0..1..0...1....0.....3......2.......9.......12........33.........56
.0..2..1...4....8....22.....47.....123......302.......784.......1961
.0..3..0...8...20....66....207.....726.....2461......8538......29072
.0..5..3..22...66...394...1417....7706....33066....162051.....742361
.0..8..2..47..207..1417...7538...53989...309136...2041378...12561807
.0.13..9.123..726..7706..53989..501126..4171831..35313591..303281789
.0.21.12.302.2461.33066.309136.4171831.43679228.535178476.6028110834
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +a(n-2)
k=3: a(n) = a(n-1) +2*a(n-2) +a(n-4) -a(n-5)
k=4: [order 16]
k=5: [order 39]
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..1..0. .0..1..1..0
..1..1..0..0. .1..0..0..1. .1..1..0..0. .1..0..0..1. .1..0..0..1
..0..0..1..1. .0..1..1..0. .0..0..1..1. .1..0..0..1. .0..1..1..0
..1..0..1..0. .0..1..1..0. .1..1..0..0. .0..1..1..0. .1..0..0..1
..0..1..0..1. .1..0..0..1. .0..1..0..1. .1..0..0..1. .0..1..1..0
CROSSREFS
Column 2 is A000045(n-1).
Sequence in context: A254218 A263147 A298100 * A073274 A192323 A242848
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 27 2018
STATUS
approved