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A300804 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 228, 128, 16, 32, 512, 1672, 1672, 512, 32, 64, 2048, 12228, 23096, 12228, 2048, 64, 128, 8192, 89472, 317504, 317504, 89472, 8192, 128, 256, 32768, 654628, 4369224, 8170504, 4369224, 654628, 32768, 256, 512, 131072 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......228........1672.........12228............89472
...8....128.....1672.......23096........317504..........4369224
..16....512....12228......317504.......8170504........210678360
..32...2048....89472.....4369224.....210678360......10189867088
..64...8192...654628....60123512....5431609016.....492720806016
.128..32768..4789672...827349312..140040313680...23826737802264
.256.131072.35044228.11385017480.3610578476036.1152195114983576
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) +3*a(n-2) -5*a(n-3)
k=4: [order 11]
k=5: [order 27] for n>29
k=6: [order 85] for n>87
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..0
..1..0..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1. .0..1..1..0
..1..0..0..1. .1..1..0..1. .1..1..1..0. .1..1..0..1. .1..0..0..1
..0..0..1..1. .1..0..0..0. .0..0..1..0. .1..0..0..1. .1..1..0..0
..1..0..1..1. .0..1..0..1. .0..0..1..1. .1..0..1..1. .0..0..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Sequence in context: A317565 A302741 A300215 * A303456 A301443 A302010
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 13 2018
STATUS
approved

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Last modified April 13 22:20 EDT 2024. Contains 371646 sequences. (Running on oeis4.)