|
| |
|
|
A317565
|
|
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 7 or 8 king-move 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, 1619, 1619, 512, 32, 64, 2048, 11510, 20312, 11510, 2048, 64, 128, 8192, 81814, 255788, 255788, 81814, 8192, 128, 256, 32768, 581541, 3218063, 5721314, 3218063, 581541, 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................64
...2......8.......32........128...........512............2048..............8192
...4.....32......228.......1619.........11510...........81814............581541
...8....128.....1619......20312........255788.........3218063..........40491721
..16....512....11510.....255788.......5721314.......127754533........2853437287
..32...2048....81814....3218063.....127754533......5059110002......200422637482
..64...8192...581541...40491721....2853437287....200422637482....14085130453968
.128..32768..4133710..509501103...63734296219...7940287015341...989910863217269
.256.131072.29383111.6410860875.1423516915862.314559200160931.69566536617221409
|
|
|
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) = 6*a(n-1) +11*a(n-2) -11*a(n-3) -72*a(n-4) -54*a(n-5) for n>6
k=4: [order 17] for n>18
k=5: [order 62] for n>63
|
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
..0..1..0..1. .1..1..1..0. .0..0..0..1. .1..0..0..1. .0..1..1..1
..0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..0. .0..1..1..1
..1..1..1..0. .1..1..1..1. .0..0..0..1. .0..0..0..0. .0..0..1..1
..1..1..0..1. .1..1..0..1. .0..0..1..0. .0..1..1..0. .0..0..1..0
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
