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A317118
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 8, 4, 8, 30, 30, 8, 16, 112, 142, 112, 16, 32, 420, 698, 698, 420, 32, 64, 1576, 3398, 5157, 3398, 1576, 64, 128, 5912, 16686, 37221, 37221, 16686, 5912, 128, 256, 22176, 81809, 273221, 392393, 273221, 81809, 22176, 256, 512, 83184, 401415
OFFSET
1,2
COMMENTS
Table starts
...1.....2.......4.........8.........16...........32.............64
...2.....8......30.......112........420.........1576...........5912
...4....30.....142.......698.......3398........16686..........81809
...8...112.....698......5157......37221.......273221........2000595
..16...420....3398.....37221.....392393......4237829.......45938893
..32..1576...16686....273221....4237829.....67247490.....1080066752
..64..5912...81809...2000595...45938893...1080066752....25956605294
.128.22176..401415..14657917..497129492..17278502991...620005212254
.256.83184.1969107.107409094.5387633738.277268412729.14887658798448
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3)
k=3: [order 10] for n>12
k=4: [order 35] for n>37
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..0. .0..1..1..0. .0..1..1..1. .0..1..0..1
..0..0..0..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .0..0..1..1
..0..1..1..1. .1..1..0..1. .1..1..1..1. .0..1..0..1. .0..0..1..1
..1..1..1..0. .0..1..1..1. .1..1..0..1. .1..1..1..1. .1..0..0..1
..1..1..0..1. .1..0..1..0. .0..1..1..0. .1..0..0..0. .0..1..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A281949.
Sequence in context: A281955 A316183 A305769 * A305530 A317004 A316822
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 21 2018
STATUS
approved