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A316176
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 16, 10, 3, 5, 51, 34, 34, 51, 5, 8, 165, 113, 72, 113, 165, 8, 13, 306, 275, 331, 331, 275, 306, 13, 21, 993, 604, 1425, 3087, 1425, 604, 993, 21, 34, 2867, 1804, 5297, 16382, 16382, 5297, 1804, 2867, 34, 55, 6818, 4683, 18573, 66575
OFFSET
1,5
COMMENTS
Table starts
..0....1....1.....2.......3.........5..........8...........13............21
..1....3...11....10......51.......165........306..........993..........2867
..1...11...16....34.....113.......275........604.........1804..........4683
..2...10...34....72.....331......1425.......5297........18573.........84658
..3...51..113...331....3087.....16382......66575.......500251.......3416740
..5..165..275..1425...16382....139293.....976178.....10070845.....106916450
..8..306..604..5297...66575....976178...12236682....164577403....2930093529
.13..993.1804.18573..500251..10070845..164577403...4139589568..113829450853
.21.2867.4683.84658.3416740.106916450.2930093529.113829450853.4957413596069
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
k=3: [order 18] for n>20
k=4: [order 64] for n>66
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..1. .0..1..1..0. .0..0..1..0. .0..0..0..0
..0..0..1..0. .0..1..0..1. .0..1..1..0. .1..0..0..0. .1..1..0..1
..1..0..1..0. .1..1..1..1. .1..1..1..1. .0..0..0..1. .0..0..0..0
..1..0..0..0. .1..1..1..0. .0..1..1..0. .0..0..1..0. .0..0..0..0
..0..0..1..0. .1..0..1..1. .0..1..1..1. .1..1..1..1. .0..1..1..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A304052.
Sequence in context: A316455 A305015 A316648 * A317458 A301615 A180771
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 25 2018
STATUS
approved