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A304767
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
7
0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 16, 18, 0, 0, 61, 103, 103, 61, 0, 0, 209, 609, 1321, 609, 209, 0, 0, 702, 3680, 14831, 14831, 3680, 702, 0, 0, 2381, 22187, 172574, 316639, 172574, 22187, 2381, 0, 0, 8069, 133917, 1999511, 6978743, 6978743, 1999511
OFFSET
1,5
COMMENTS
Table starts
.0....0......0.........0...........0..............0................0
.0....3......5........18..........61............209..............702
.0....5.....16.......103.........609...........3680............22187
.0...18....103......1321.......14831.........172574..........1999511
.0...61....609.....14831......316639........6978743........153265405
.0..209...3680....172574.....6978743......292676592......12219307955
.0..702..22187...1999511...153265405....12219307955.....969267512820
.0.2381.133917..23203301..3370551763...510976436144...77018325396680
.0.8069.808316.269239457.74123574757.21366609684109.6119460744287122
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 13] for n>15
k=4: [order 31] for n>32
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..1..0..0. .0..1..1..0. .0..1..0..0. .0..1..1..0
..1..1..1..0. .0..1..1..1. .1..1..0..1. .1..1..1..1. .1..0..1..1
..0..1..1..1. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..0..1
..1..1..0..1. .1..1..1..0. .1..0..1..1. .1..0..1..0. .1..0..0..0
..0..0..1..0. .0..1..0..1. .0..1..1..0. .0..1..1..0. .0..1..1..1
CROSSREFS
Column 2 is A303684.
Sequence in context: A305457 A305022 A316686 * A316511 A317465 A051174
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 18 2018
STATUS
approved