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A283857
T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.
13
2, 4, 4, 8, 16, 8, 16, 61, 64, 16, 32, 233, 409, 256, 32, 64, 896, 2776, 2837, 1024, 64, 128, 3444, 19220, 35373, 19776, 4096, 128, 256, 13225, 131617, 456316, 448490, 137459, 16384, 256, 512, 50789, 901397, 5742620, 10741381, 5676420, 955680, 65536, 512
OFFSET
1,1
COMMENTS
Table starts
...2.....4.......8........16...........32.............64..............128
...4....16......61.......233..........896...........3444............13225
...8....64.....409......2776........19220.........131617...........901397
..16...256....2837.....35373.......456316........5742620.........72394838
..32..1024...19776....448490.....10741381......247708452.......5724272337
..64..4096..137459...5676420....252014450....10634931992.....449942735521
.128.16384..955680..71903903...5921518755...457711375590...35481195059121
.256.65536.6645662.910712188.139111379622.19691576356912.2796411775700471
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: [order 8]
k=4: [order 17]
k=5: [order 45]
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +a(n-2) +7*a(n-3) +6*a(n-4)
n=3: [order 14]
n=4: [order 28]
n=5: [order 74]
EXAMPLE
Some solutions for n=4 k=4
..1..0..0..1. .0..0..1..0. .1..1..1..1. .0..0..0..0. .1..0..1..1
..0..1..1..0. .1..0..0..0. .0..1..0..0. .0..0..0..1. .1..0..1..1
..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..1
..1..1..0..0. .1..0..0..0. .1..0..0..1. .1..1..0..1. .1..1..0..1
CROSSREFS
Column 1 is A000079.
Column 2 is A000302.
Row 1 is A000079.
Sequence in context: A297374 A297102 A283415 * A227442 A282316 A228986
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 17 2017
STATUS
approved