|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|