|
| |
|
|
A299844
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.
|
|
5
|
|
|
|
1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 163, 121, 16, 32, 472, 927, 927, 472, 32, 64, 1841, 5331, 8245, 5331, 1841, 64, 128, 7181, 30535, 74329, 74329, 30535, 7181, 128, 256, 28010, 175286, 664377, 1056001, 664377, 175286, 28010, 256, 512, 109255, 1006611
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Table starts
...1......2.......4.........8..........16............32..............64
...2......8......31.......121.........472..........1841............7181
...4.....31.....163.......927........5331.........30535..........175286
...8....121.....927......8245.......74329........664377.........5966905
..16....472....5331.....74329.....1056001......14831535.......209649848
..32...1841...30535....664377....14831535.....325878154......7216925214
..64...7181..175286...5966905...209649848....7216925214....250915415042
.128..28010.1006611..53667656..2971226455..160460196001...8769920586285
.256.109255.5780036.482603686.42097006186.3565906147902.306309096924610
|
|
|
LINKS
|
R. H. Hardin, Table of n, a(n) for n = 1..180
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +3*a(n-2) +2*a(n-3)
k=3: [order 10] for n>11
k=4: [order 30] for n>31
|
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..0. .0..0..1..1. .0..0..0..1. .0..0..0..0
..0..0..0..1. .1..0..1..1. .1..0..0..1. .1..1..1..1. .1..1..1..0
..1..1..0..1. .1..0..0..0. .1..1..0..1. .0..0..0..0. .0..0..0..1
..1..0..0..1. .0..1..1..1. .0..1..0..1. .0..1..1..1. .0..1..0..0
..1..0..1..1. .1..0..1..1. .0..0..1..0. .0..0..0..1. .0..1..0..1
|
|
|
CROSSREFS
|
Column 1 is A000079(n-1).
Column 2 is A281831.
Column 3 is A299076.
Column 4 is A299077.
Sequence in context: A317572 A281837 A299081 * A299001 A299746 A299668
Adjacent sequences: A299841 A299842 A299843 * A299845 A299846 A299847
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
R. H. Hardin, Feb 20 2018
|
|
|
STATUS
|
approved
|
| |
|
|
