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A305245
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 8 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 18, 24, 16, 32, 64, 32, 32, 64, 32, 64, 184, 86, 94, 86, 184, 64, 128, 432, 158, 273, 273, 158, 432, 128, 256, 1088, 343, 767, 1134, 767, 343, 1088, 256, 512, 2944, 721, 2128, 3288, 3288, 2128, 721, 2944, 512, 1024, 7360, 1520
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...18....32.....86.....158.....343......721......1520.......3228
...8...24...32....94....273.....767....2128.....6150.....17387......49477
..16...64...86...273...1134....3288...11731....39986....136448.....468584
..32..184..158...767...3288...12521...55039...238455...1028982....4474894
..64..432..343..2128..11731...55039..311014..1742187...9652212...54215925
.128.1088..721..6150..39986..238455.1742187.12726939..91021791..667854447
.256.2944.1520.17387.136448.1028982.9652212.91021791.841464188.8000379451
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 8] for n>11
k=4: [order 28] for n>32
k=5: [order 34] for n>42
k=6: [order 98] for n>104
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..1..0. .1..1..1..1
..1..0..1..1. .0..0..0..0. .1..0..0..1. .0..0..0..0. .1..1..1..1
..0..1..1..1. .0..1..0..0. .0..0..0..1. .0..0..0..0. .1..1..1..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A303794.
Sequence in context: A320196 A033740 A303800 * A304479 A316304 A304848
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 28 2018
STATUS
approved