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A296578
T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.
8
2, 4, 4, 7, 11, 7, 13, 31, 31, 13, 24, 90, 135, 90, 24, 44, 254, 616, 616, 254, 44, 81, 728, 2782, 4543, 2782, 728, 81, 149, 2078, 12544, 32439, 32439, 12544, 2078, 149, 274, 5931, 56646, 233636, 368720, 233636, 56646, 5931, 274, 504, 16941, 255699, 1680927
OFFSET
1,1
COMMENTS
Table starts
...2.....4.......7.......13.........24...........44.............81
...4....11......31.......90........254..........728...........2078
...7....31.....135......616.......2782........12544..........56646
..13....90.....616.....4543......32439.......233636........1680927
..24...254....2782....32439.....368720......4215593.......48217515
..44...728...12544...233636....4215593.....76657600.....1394258872
..81..2078...56646..1680927...48217515...1394258872....40337678992
.149..5931..255699.12090311..551193737..25339030733..1165868818808
.274.16941.1154239.86993766.6302520826.460672241848.33712843195488
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
k=2: a(n) = a(n-1) +4*a(n-2) +3*a(n-3) +a(n-4) +4*a(n-5) -a(n-6) -6*a(n-7) -a(n-8) +a(n-9)
k=3: [order 14]
k=4: [order 50]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..0..0..1. .1..0..0..0. .0..1..0..0. .0..0..1..0
..1..0..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..0. .1..1..0..0
..0..1..0..1. .1..0..0..1. .0..1..0..0. .0..0..0..0. .0..1..0..0
..0..0..0..0. .0..1..0..0. .0..1..0..1. .1..0..0..1. .0..0..1..0
..0..0..1..1. .0..0..1..0. .0..0..0..1. .1..0..0..0. .1..0..1..0
CROSSREFS
Column 1 is A000073(n+3).
Sequence in context: A282647 A269089 A282862 * A268750 A282996 A295275
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 15 2017
STATUS
approved