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A317458
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 17, 10, 3, 5, 51, 36, 36, 51, 5, 8, 165, 131, 72, 131, 165, 8, 13, 306, 322, 353, 353, 322, 306, 13, 21, 993, 762, 1525, 4364, 1525, 762, 993, 21, 34, 2867, 2337, 5601, 21250, 21250, 5601, 2337, 2867, 34, 55, 6818, 6165, 20603, 95144
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...17....36.....131.......322........762.........2337..........6165
..2...10...36....72.....353......1525.......5601........20603.........93180
..3...51..131...353....4364.....21250......95144.......744225.......4783771
..5..165..322..1525...21250....165890....1201543.....12609827.....130759485
..8..306..762..5601...95144...1201543...14872138....206130149....3590280962
.13..993.2337.20603..744225..12609827..206130149...5301169782..141656940788
.21.2867.6165.93180.4783771.130759485.3590280962.141656940788.6077202952491
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..0..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..1..0. .1..0..0..0. .1..0..0..1. .1..0..0..1. .0..1..0..0
..1..0..1..0. .1..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..0..0..0. .1..1..1..0. .1..0..0..1. .1..0..0..0. .1..0..0..1
..0..0..1..0. .1..0..1..1. .1..0..0..0. .0..0..1..0. .1..0..0..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A304052.
Sequence in context: A305015 A316648 A316176 * A301615 A180771 A300546
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 28 2018
STATUS
approved