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A318552
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 3, 1, 2, 6, 6, 2, 3, 10, 5, 10, 3, 5, 21, 21, 21, 21, 5, 8, 46, 44, 64, 44, 46, 8, 13, 102, 106, 219, 219, 106, 102, 13, 21, 220, 258, 589, 842, 589, 258, 220, 21, 34, 491, 600, 1782, 3172, 3172, 1782, 600, 491, 34, 55, 1077, 1476, 5621, 12073, 14760, 12073, 5621
OFFSET
1,5
COMMENTS
Table starts
..0...1....1.....2......3.......5........8........13.........21..........34
..1...3....6....10.....21......46......102.......220........491........1077
..1...6....5....21.....44.....106......258.......600.......1476........3461
..2..10...21....64....219.....589.....1782......5621......17333.......54199
..3..21...44...219....842....3172....12073.....49181.....191426......766695
..5..46..106...589...3172...14760....67976....337349....1614708.....7855731
..8.102..258..1782..12073...67976...437825...2689769...16069287...100151409
.13.220..600..5621..49181..337349..2689769..21556643..159367978..1242485030
.21.491.1476.17333.191426.1614708.16069287.159367978.1516492860.14741167613
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +4*a(n-2) -2*a(n-3) -2*a(n-4) +a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)
k=3: [order 31]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..1..1. .0..0..1..0. .0..0..0..0. .0..1..1..0
..1..0..0..0. .1..1..0..1. .1..0..0..0. .1..1..0..1. .1..1..0..1
..0..0..1..1. .1..0..0..1. .0..0..1..1. .1..0..0..0. .1..1..0..0
..1..0..1..1. .0..0..0..1. .0..1..0..1. .1..1..0..1. .0..0..0..1
..0..1..1..0. .1..1..1..0. .1..0..0..1. .1..0..0..0. .0..1..0..0
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A317857.
Sequence in context: A360634 A317863 A318214 * A183289 A183253 A201675
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 28 2018
STATUS
approved