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A296674
T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 3 king-move neighboring 1s.
8
2, 3, 3, 5, 10, 5, 8, 25, 25, 8, 13, 68, 82, 68, 13, 21, 208, 334, 334, 208, 21, 34, 609, 1451, 2295, 1451, 609, 34, 55, 1785, 5938, 16541, 16541, 5938, 1785, 55, 89, 5375, 25144, 110036, 213800, 110036, 25144, 5375, 89, 144, 16174, 108174, 775010, 2358963
OFFSET
1,1
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +5*a(n-3) -10*a(n-4) -12*a(n-5) -4*a(n-6)
k=3: [order 12]
k=4: [order 27]
k=5: [order 67]
EXAMPLE
Table starts
..2.....3......5........8.........13...........21.............34
..3....10.....25.......68........208..........609...........1785
..5....25.....82......334.......1451.........5938..........25144
..8....68....334.....2295......16541.......110036.........775010
.13...208...1451....16541.....213800......2358963.......28341757
.21...609...5938...110036....2358963.....40937523......794602323
.34..1785..25144...775010...28341757....794602323....25499216805
.55..5375.108174..5466936..346828018..15702927104...833656369935
.89.16174.463106.38297415.4150012532.301022037125.26222808591554
...
Some solutions for n=4 k=4
..1..1..1..0. .0..0..0..0. .0..1..1..0. .0..1..0..0. .0..0..1..1
..1..0..0..1. .1..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1
..1..0..1..0. .0..0..0..0. .0..0..0..0. .1..0..0..1. .1..1..1..0
..1..1..0..0. .1..0..0..1. .1..0..0..1. .1..1..0..0. .1..0..0..0
CROSSREFS
Column 1 is A000045(n+2).
Sequence in context: A175147 A001180 A228778 * A297073 A019460 A329057
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 18 2017
STATUS
approved