|
|
A298622
|
|
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
|
|
7
|
|
|
0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 16, 0, 16, 0, 1, 48, 7, 7, 48, 1, 0, 88, 7, 83, 7, 88, 0, 1, 240, 25, 218, 218, 25, 240, 1, 0, 704, 88, 682, 1893, 682, 88, 704, 0, 1, 1600, 187, 4068, 5749, 5749, 4068, 187, 1600, 1, 0, 4032, 491, 14719, 51213, 32834, 51213, 14719, 491, 4032
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
Table starts
.0....1...0.....1.......0........1..........0...........1.............0
.1....4...4....16......48.......88........240.........704..........1600
.0....4...0.....7.......7.......25.........88.........187...........491
.1...16...7....83.....218......682.......4068.......14719.........58834
.0...48...7...218....1893.....5749......51213......407430.......2021867
.1...88..25...682....5749....32834.....480343.....4361690......38698593
.0..240..88..4068...51213...480343...10823065...161922923....2400592063
.1..704.187.14719..407430..4361690..161922923..4673855921...92707820639
.0.1600.491.58834.2021867.38698593.2400592063.92707820639.3376311711594
|
|
LINKS
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = a(n-2)
k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)
k=3: [order 19] for n>20
k=4: [order 64] for n>65
|
|
EXAMPLE
|
Some solutions for n=5 k=4
..0..0..0..1. .0..1..0..0. .0..0..0..1. .0..0..1..1. .0..1..1..1
..0..0..1..0. .0..1..0..0. .0..0..1..0. .0..0..1..1. .1..0..1..1
..1..1..1..1. .1..1..0..0. .1..1..1..1. .0..0..1..1. .1..1..1..1
..0..0..1..0. .1..1..1..1. .1..1..0..1. .1..0..1..1. .1..0..0..0
..0..0..0..1. .0..0..1..1. .1..1..1..0. .1..0..1..1. .0..1..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|