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A299060
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
7
1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 38, 42, 1, 1, 127, 199, 199, 127, 1, 1, 389, 864, 2096, 864, 389, 1, 1, 1192, 4366, 17930, 17930, 4366, 1192, 1, 1, 3645, 21804, 175031, 295407, 175031, 21804, 3645, 1, 1, 11161, 111861, 1718789, 5558665, 5558665
OFFSET
1,5
COMMENTS
Table starts
.1....1......1........1..........1............1..............1................1
.1....5.....13.......42........127..........389...........1192.............3645
.1...13.....38......199........864.........4366..........21804...........111861
.1...42....199.....2096......17930.......175031........1718789.........17101477
.1..127....864....17930.....295407......5558665......104819165.......1992248544
.1..389...4366...175031....5558665....199153610.....7165136807.....259511787831
.1.1192..21804..1718789..104819165...7165136807...491688804213...33934925502793
.1.3645.111861.17101477.1992248544.259511787831.33934925502793.4462148033879670
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +5*a(n-2) +4*a(n-3)
k=3: [order 14] for n>16
k=4: [order 38] for n>39
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..1. .0..0..1..1. .0..0..1..0. .0..1..0..0
..0..1..1..1. .0..0..1..1. .1..0..1..1. .0..0..1..1. .0..0..0..1
..1..1..0..1. .1..0..0..0. .0..0..1..0. .0..0..1..1. .1..1..0..0
..1..1..1..1. .1..1..0..1. .1..0..0..0. .0..0..0..1. .0..1..1..0
..0..1..0..1. .1..1..1..1. .0..0..0..1. .0..1..0..0. .0..0..0..0
CROSSREFS
Column 2 is A298234.
Sequence in context: A299366 A299135 A299893 * A299821 A299721 A300342
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 01 2018
STATUS
approved