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A304479
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.
7
1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 19, 24, 16, 32, 64, 37, 37, 64, 32, 64, 184, 94, 110, 94, 184, 64, 128, 432, 202, 297, 297, 202, 432, 128, 256, 1088, 428, 869, 931, 869, 428, 1088, 256, 512, 2944, 965, 2325, 2870, 2870, 2325, 965, 2944, 512, 1024, 7360, 2134
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...19....37....94....202.....428......965.....2134......4692
...8...24...37...110...297....869....2325.....6379....17568.....48401
..16...64...94...297...931...2870....8058....25040....76568....231646
..32..184..202...869..2870..11079...35462...133597...471114...1710896
..64..432..428..2325..8058..35462..132348...573938..2341508...9662652
.128.1088..965..6379.25040.133597..573938..2942145.13964485..67899747
.256.2944.2134.17568.76568.471114.2341508.13964485.77098563.429574178
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..1..1..0. .0..0..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..0
..0..1..1..0. .0..0..1..1. .0..0..0..1. .1..0..1..0. .0..0..0..1
..1..1..1..1. .0..1..1..1. .0..0..0..1. .0..0..0..1. .0..0..0..0
..1..1..1..1. .0..1..1..0. .1..0..0..0. .1..0..1..1. .1..0..0..0
..1..1..1..1. .1..1..1..0. .0..1..0..0. .1..0..1..1. .0..1..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A303794.
Sequence in context: A033740 A303800 A305245 * A316304 A304848 A316545
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 13 2018
STATUS
approved