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.

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

Offset: 1

Author

R. H. Hardin, Jan 28 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..312

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297852.

Column 3 is A298050.

Column 4 is A298051.

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