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A297907 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 king-move adjacent elements, with upper left element zero. 8
1, 2, 2, 3, 4, 3, 5, 3, 3, 5, 8, 13, 1, 13, 8, 13, 34, 4, 4, 34, 13, 21, 73, 5, 37, 5, 73, 21, 34, 203, 5, 54, 54, 5, 203, 34, 55, 594, 20, 97, 281, 97, 20, 594, 55, 89, 1443, 29, 466, 395, 395, 466, 29, 1443, 89, 144, 4013, 63, 1105, 2353, 257, 2353, 1105, 63, 4013, 144, 233 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1....2..3....5.....8....13.....21......34.......55........89........144
..2....4..3...13....34....73....203.....594.....1443......4013......11114
..3....3..1....4.....5.....5.....20......29.......63.......156........311
..5...13..4...37....54....97....466....1105.....3354.....12282......37107
..8...34..5...54...281...395...2353...12834....42557....215887....1120924
.13...73..5...97...395...257...1586....5761....18420.....89795.....363173
.21..203.20..466..2353..1586..23911..117161...369290...3815083...22352269
.34..594.29.1105.12834..5761.117161.1367645..4265928..59508287..657006826
.55.1443.63.3354.42557.18420.369290.4265928.10485521.149524668.1517719548
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
k=3: [order 12] for n>13
k=4: [order 48] for n>51
EXAMPLE
Some solutions for n=7 k=4
..0..1..0..1. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..0..1
..1..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .1..1..0..0
..1..1..0..1. .0..1..1..1. .1..1..0..1. .1..1..0..1. .1..1..0..1
..0..1..0..1. .1..0..1..0. .1..0..0..1. .0..1..0..1. .0..1..0..0
..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0
..1..1..0..1. .1..0..1..1. .1..1..1..0. .1..1..0..1. .1..1..1..1
..0..1..1..0. .1..0..1..1. .0..1..0..1. .1..1..0..1. .0..1..0..0
CROSSREFS
Column 1 is A000045(n+1).
Sequence in context: A080046 A047675 A187199 * A298501 A298320 A299393
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 08 2018
STATUS
approved

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Last modified May 24 14:39 EDT 2024. Contains 372778 sequences. (Running on oeis4.)