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A298719
T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.
7
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 5, 4, 5, 0, 0, 10, 13, 13, 10, 0, 0, 25, 63, 59, 63, 25, 0, 0, 54, 264, 346, 346, 264, 54, 0, 0, 125, 1005, 2246, 3508, 2246, 1005, 125, 0, 0, 282, 4113, 13650, 34704, 34704, 13650, 4113, 282, 0, 0, 641, 16720, 87117, 309593, 563977
OFFSET
1,8
COMMENTS
Table starts
.0...0.....0......0........0..........0............0.............0
.0...1.....2......5.......10.........25...........54...........125
.0...2.....4.....13.......63........264.........1005..........4113
.0...5....13.....59......346.......2246........13650.........87117
.0..10....63....346.....3508......34704.......309593.......2960634
.0..25...264...2246....34704.....563977......8287084.....125919136
.0..54..1005..13650...309593....8287084....193439202....4672566734
.0.125..4113..87117..2960634..125919136...4672566734..177476979652
.0.282.16720.550582.27934888.1909040369.112689610775.6748480839625
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-2) +4*a(n-3) +2*a(n-4)
k=3: [order 18]
k=4: [order 63] for n>64
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..1. .0..1..1..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..0..1..1
..1..0..0..0. .0..1..0..0. .1..1..0..0. .0..1..0..1. .0..1..0..1
..0..1..1..0. .1..0..0..1. .1..0..0..1. .1..0..1..1. .1..0..0..1
..0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
CROSSREFS
Column 2 is A297860.
Sequence in context: A297866 A298133 A298070 * A296148 A121178 A175917
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 25 2018
STATUS
approved