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A316304
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 20, 24, 16, 32, 64, 39, 39, 64, 32, 64, 184, 110, 114, 110, 184, 64, 128, 432, 245, 339, 339, 245, 432, 128, 256, 1088, 572, 1021, 1519, 1021, 572, 1088, 256, 512, 2944, 1384, 2929, 5120, 5120, 2929, 1384, 2944, 512, 1024, 7360
OFFSET
1,2
COMMENTS
Table starts
...1....2....4.....8.....16......32.......64.......128........256.........512
...2....4...12....24.....64.....184......432......1088.......2944........7360
...4...12...20....39....110.....245......572......1384.......3267........7767
...8...24...39...114....339....1021.....2929......8639......25410.......74617
..16...64..110...339...1519....5120....19185.....72289.....268933......999260
..32..184..245..1021...5120...20780....97864....444290....2065314.....9512624
..64..432..572..2929..19185...97864...608947...3605691...21632912...130126938
.128.1088.1384..8639..72289..444290..3605691..26898537..208808616..1617004105
.256.2944.3267.25410.268933.2065314.21632912.208808616.2095245767.21106046766
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6
k=3: [order 12] for n>13
k=4: [order 65] for n>67
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..0. .0..0..0..0. .0..1..1..0. .0..0..1..0
..1..1..1..1. .0..1..0..0. .1..0..1..1. .0..0..0..0. .0..0..0..1
..1..1..1..0. .1..0..0..0. .0..1..1..1. .0..0..0..0. .1..0..0..0
..1..1..0..1. .1..1..0..0. .1..1..1..1. .1..0..1..1. .1..0..0..1
..0..0..0..0. .1..0..1..0. .1..1..1..1. .0..1..1..1. .0..0..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A303794.
Sequence in context: A303800 A305245 A304479 * A304848 A316545 A306060
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 29 2018
STATUS
approved