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A297866
T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.
8
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 5, 4, 5, 0, 0, 10, 13, 13, 10, 0, 0, 25, 62, 15, 62, 25, 0, 0, 54, 222, 233, 233, 222, 54, 0, 0, 125, 820, 1052, 2621, 1052, 820, 125, 0, 0, 282, 3159, 5774, 21519, 21519, 5774, 3159, 282, 0, 0, 641, 11882, 36119, 174970, 284344, 174970
OFFSET
1,8
COMMENTS
Table starts
.0...0.....0......0........0.........0...........0.............0..............0
.0...1.....2......5.......10........25..........54...........125............282
.0...2.....4.....13.......62.......222.........820..........3159..........11882
.0...5....13.....15......233......1052........5774.........36119.........204522
.0..10....62....233.....2621.....21519......174970.......1556367.......13214094
.0..25...222...1052....21519....284344.....3740362......52727368......711614693
.0..54...820...5774...174970...3740362....76517448....1699781649....36000744495
.0.125..3159..36119..1556367..52727368..1699781649...58344517697..1923723833047
.0.282.11882.204522.13214094.711614693.36000744495.1923723833047.99045666327382
LINKS
FORMULA
Empirical for column k:
k=1: a(n) =
k=2: a(n) = 3*a(n-2) +4*a(n-3) +2*a(n-4)
k=3: [order 14] for n>16
k=4: [order 47] for n>50
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..1
..0..1..0..1. .0..1..1..0. .1..0..1..1. .1..0..0..1. .0..1..0..1
..0..1..1..1. .1..1..0..1. .1..1..0..0. .1..1..1..1. .0..0..1..0
..1..0..0..0. .1..0..0..1. .1..0..0..1. .0..1..0..0. .0..1..1..0
..1..1..0..0. .1..1..1..1. .0..0..1..1. .0..0..0..0. .1..1..0..0
CROSSREFS
Sequence in context: A330619 A245693 A370374 * A298133 A298070 A298719
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 07 2018
STATUS
approved