|
|
A298888
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
|
|
5
|
|
|
0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 19, 19, 23, 5, 8, 49, 23, 40, 23, 49, 8, 13, 95, 34, 73, 73, 34, 95, 13, 21, 177, 63, 141, 123, 141, 63, 177, 21, 34, 359, 96, 240, 243, 243, 240, 96, 359, 34, 55, 705, 147, 428, 444, 516, 444, 428, 147, 705, 55, 89, 1351, 233
(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.....55.....89.....144.....233
..1...3...7..13...23...49...95...177...359...705...1351...2689....5303...10321
..1...7..15..19...23...34...63....96...147...233....368....588.....933....1500
..2..13..19..40...73..141..240...428...779..1531...2989...5729...10760...20205
..3..23..23..73..123..243..444...897..1801..3462...6669..13291...25762...49483
..5..49..34.141..243..516..814..1646..3312..6565..13040..25941...51679..103895
..8..95..63.240..444..814.1818..3663..7496.16544..33596..70466..148451..311053
.13.177..96.428..897.1646.3663..7768.17225.39617..83996.184024..411042..903972
.21.359.147.779.1801.3312.7496.17225.41048.95996.221358.505218.1183870.2737277
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6
k=3: [order 18] for n>19
k=4: [order 72] for n>73
|
|
EXAMPLE
|
Some solutions for n=7 k=5
..0..1..0..0..0. .0..1..0..1..1. .0..0..1..0..1. .0..1..1..0..1
..0..0..1..1..1. .1..0..0..1..0. .1..0..1..1..0. .1..0..0..0..1
..0..0..0..0..0. .0..1..1..1..0. .1..0..0..0..1. .1..0..0..0..1
..1..0..0..0..1. .0..1..1..1..0. .1..0..0..0..1. .0..0..0..0..0
..1..0..0..0..1. .1..1..1..1..1. .0..0..0..0..0. .1..1..1..0..0
..0..1..1..0..1. .1..1..0..0..0. .1..1..1..0..0. .0..0..0..0..1
..1..0..1..0..0. .1..0..1..1..1. .0..0..0..1..0. .1..1..1..0..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|