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A305692
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 152, 98, 3, 5, 383, 1151, 1151, 383, 5, 8, 1493, 8415, 16658, 8415, 1493, 8, 13, 5824, 61796, 236246, 236246, 61796, 5824, 13, 21, 22717, 453553, 3346848, 6433903, 3346848, 453553, 22717, 21, 34, 88609, 3329201
OFFSET
1,5
COMMENTS
Table starts
..0.....1........1..........2.............3................5..................8
..1.....7.......25.........98...........383.............1493...............5824
..1....25......152.......1151..........8415............61796.............453553
..2....98.....1151......16658........236246..........3346848...........47448563
..3...383.....8415.....236246.......6433903........175572754.........4791219558
..5..1493....61796....3346848.....175572754.......9226209199.......484920924010
..8..5824...453553...47448563....4791219558.....484920924010.....49083436693252
.13.22717..3329201..672609073..130750175963...25486278629503...4968168200482612
.21.88609.24436772.9534641574.3568076221953.1339494303168987.502868587709213674
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +3*a(n-2) +2*a(n-3)
k=3: a(n) = 6*a(n-1) +8*a(n-2) +12*a(n-3) +11*a(n-4) -a(n-5) +a(n-6) +a(n-7) -a(n-8)
k=4: [order 17]
k=5: [order 52]
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..1. .0..0..0..0. .0..0..1..0. .0..0..0..1
..1..0..0..1. .1..0..0..0. .1..1..1..1. .0..1..1..0. .0..1..0..1
..1..0..0..1. .0..0..0..0. .0..0..0..1. .1..0..0..1. .1..0..1..1
..0..1..0..0. .0..0..0..1. .1..1..1..0. .1..0..1..0. .0..0..1..1
..1..1..1..0. .1..0..0..1. .1..0..0..0. .1..0..1..1. .0..1..1..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A304421.
Sequence in context: A316282 A305961 A317222 * A317072 A316953 A317733
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 08 2018
STATUS
approved