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A316693 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 3, 3, 8, 16, 5, 8, 5, 16, 32, 8, 9, 9, 8, 32, 64, 13, 21, 23, 21, 13, 64, 128, 21, 42, 44, 44, 42, 21, 128, 256, 34, 81, 125, 88, 125, 81, 34, 256, 512, 55, 165, 313, 359, 359, 313, 165, 55, 512, 1024, 89, 330, 773, 1125, 2081, 1125, 773, 330, 89, 1024, 2048 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1..2...4....8....16.....32......64......128.......256........512........1024
...2..4...3....5.....8.....13......21.......34........55.........89.........144
...4..3...8....9....21.....42......81......165.......330........657........1317
...8..5...9...23....44....125.....313......773......1964.......4948.......12456
..16..8..21...44....88....359....1125.....3117.....10022......31545.......95424
..32.13..42..125...359...2081....9442....38020....174483.....785604.....3427907
..64.21..81..313..1125...9442...61454...342508...2212378...14109348....86477928
.128.34.165..773..3117..38020..342508..2431114..21261766..184273462..1497908640
.256.55.330.1964.10022.174483.2212378.21261766.257262996.3099570150.34685951835
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = a(n-1) +a(n-2) for n>4
k=3: a(n) = a(n-1) +a(n-2) +2*a(n-3) for n>6
k=4: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +a(n-4) -2*a(n-5) -6*a(n-6) -4*a(n-7) for n>11
k=5: [order 7] for n>11
k=6: [order 16] for n>21
k=7: [order 46] for n>52
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..1..1..0. .0..1..1..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
..1..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..1..0
..1..1..1..1. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A000045(n+1).
Sequence in context: A304230 A305586 A305040 * A230014 A319414 A303961
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 10 2018
STATUS
approved

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Last modified June 23 04:27 EDT 2024. Contains 373629 sequences. (Running on oeis4.)