|
| |
|
|
A298653
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.
|
|
5
|
|
|
|
0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 424, 466, 424, 573, 8, 13, 1933, 1274, 1446, 1446, 1274, 1933, 13, 21, 6538, 3820, 4648, 5124, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18271, 18271, 14888, 11529, 22165, 34
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
COMMENTS
|
Table starts
..0.....1.....1......2......3.......5........8........13.........21.........34
..1.....4....17.....49....166.....573.....1933......6538......22165......75089
..1....17....48....146....424....1274.....3820.....11529......34783.....104826
..2....49...146....466...1446....4648....14888.....47399.....150849.....480015
..3...166...424...1446...5124...18271....62544....215035.....739962....2537660
..5...573..1274...4648..18271...75562...291784...1142188....4518674...17656883
..8..1933..3820..14888..62544..291784..1277500...5758443...26328879..118276552
.13..6538.11529..47399.215035.1142188..5758443..30337435..163931288..865848465
.21.22165.34783.150849.739962.4518674.26328879.163931288.1060912744.6689007779
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 11] for n>13
k=4: [order 24] for n>27
|
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..0. .0..1..0..0. .0..1..1..0. .0..0..1..0
..1..1..1..0. .0..1..0..1. .1..0..1..0. .1..0..0..0. .1..0..1..0
..1..0..0..1. .1..1..0..1. .1..0..1..1. .0..1..1..1. .1..1..1..0
..0..1..1..1. .0..1..0..1. .1..0..0..0. .0..0..0..1. .1..0..1..0
..0..0..0..0. .0..0..1..1. .0..1..1..1. .1..1..1..0. .1..0..1..0
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
