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A296651
T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 1 or 3 king-move neighboring 1s.
8
2, 4, 4, 7, 12, 7, 13, 29, 29, 13, 24, 85, 111, 85, 24, 44, 248, 468, 468, 248, 44, 81, 664, 1985, 3159, 1985, 664, 81, 149, 1897, 8126, 20782, 20782, 8126, 1897, 149, 274, 5385, 33933, 130303, 212537, 130303, 33933, 5385, 274, 504, 14924, 141664, 849983
OFFSET
1,1
COMMENTS
Table starts
...2.....4......7.......13.........24...........44............81
...4....12.....29.......85........248..........664..........1897
...7....29....111......468.......1985.........8126.........33933
..13....85....468.....3159......20782.......130303........849983
..24...248...1985....20782.....212537......2022756......20337282
..44...664...8126...130303....2022756.....29547816.....453231742
..81..1897..33933...849983...20337282....453231742...10730354337
.149..5385.141664..5499124..202790850...6893592668..250993766141
.274.14924.588156.35347256.1998068553.103949473092.5814109226770
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) +3*a(n-2) +9*a(n-3) -4*a(n-4) -12*a(n-5) -4*a(n-6)
k=3: [order 10]
k=4: [order 22]
k=5: [order 58]
EXAMPLE
Some solutions for n=4 k=4
..1..0..1..0. .1..0..1..1. .1..1..0..1. .0..0..1..0. .1..0..0..1
..1..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..1
..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0
..1..1..0..0. .0..0..1..0. .1..0..1..1. .0..0..0..0. .0..0..0..0
CROSSREFS
Column 1 is A000073(n+3).
Sequence in context: A227089 A225900 A227558 * A297085 A224158 A224409
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 17 2017
STATUS
approved