|
| |
|
|
A316960
|
|
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
|
|
7
|
|
|
|
1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 220, 128, 16, 32, 512, 1498, 1498, 512, 32, 64, 2048, 10243, 16976, 10243, 2048, 64, 128, 8192, 70037, 194917, 194917, 70037, 8192, 128, 256, 32768, 478941, 2232443, 3796326, 2232443, 478941, 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......220.......1498........10243..........70037............478941
...8....128.....1498......16976.......194917........2232443..........25592081
..16....512....10243.....194917......3796326.......73529753........1426910760
..32...2048....70037....2232443.....73529753.....2402722112.......78728223139
..64...8192...478941...25592081...1426910760....78728223139.....4359094468163
.128..32768..3275421..293396247..27687032205..2579211359302...241311689147759
.256.131072.22400407.3363774685.537290478883.84510945441118.13360998189431905
|
|
|
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) +9*a(n-2) -14*a(n-3) -52*a(n-4) -33*a(n-5) for n>6
k=4: [order 16] for n>17
k=5: [order 58] for n>59
|
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..0..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .1..0..0..0. .0..1..1..1. .1..0..0..1. .1..0..1..1
..0..0..1..0. .1..1..1..1. .1..1..1..0. .1..1..0..1. .1..0..1..1
..1..1..0..0. .0..1..1..1. .1..1..1..0. .0..1..0..0. .0..0..0..1
..1..1..1..1. .0..1..0..0. .0..1..1..1. .0..0..1..0. .0..0..0..0
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
