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A299366
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
7
1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 23, 42, 1, 1, 127, 125, 125, 127, 1, 1, 389, 420, 1157, 420, 389, 1, 1, 1192, 1943, 8134, 8134, 1943, 1192, 1, 1, 3645, 9012, 66668, 107653, 66668, 9012, 3645, 1, 1, 11161, 42321, 564283, 1640199, 1640199, 564283, 42321
OFFSET
1,5
COMMENTS
Table starts
.1.....1......1........1..........1.............1...............1
.1.....5.....13.......42........127...........389............1192
.1....13.....23......125........420..........1943............9012
.1....42....125.....1157.......8134.........66668..........564283
.1...127....420.....8134.....107653.......1640199........25838859
.1...389...1943....66668....1640199......45416563......1301827631
.1..1192...9012...564283...25838859....1301827631.....67756659422
.1..3645..42321..4792366..404080073...37042505019...3508332244817
.1.11161.205597.41273307.6401182687.1066728270636.183583736926115
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 12] for n>14
k=4: [order 46] for n>48
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0
..1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .0..1..1..0. .1..1..1..1. .1..1..1..1. .0..0..0..0
CROSSREFS
Column 2 is A298234.
Sequence in context: A272644 A157177 A298240 * A299135 A299893 A299060
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 08 2018
STATUS
approved