A240656 T(n,k)=Number of nXk 0..1 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..1 introduced in row major order.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 9, 3, 1, 1, 6, 17, 17, 6, 1, 1, 10, 43, 91, 43, 10, 1, 1, 21, 136, 352, 352, 136, 21, 1, 1, 42, 402, 1545, 2456, 1545, 402, 42, 1, 1, 86, 1180, 7154, 16629, 16629, 7154, 1180, 86, 1, 1, 179, 3518, 33269, 118863, 184819, 118863, 33269, 3518

Offset: 1

Author

R. H. Hardin, Apr 09 2014

Keywords

• nonn
• tabl

Comments

Table starts

.1...1.....1......1........1..........1............1..............1

.1...2.....2......3........6.........10...........21.............42

.1...2.....9.....17.......43........136..........402...........1180

.1...3....17.....91......352.......1545.........7154..........33269

.1...6....43....352.....2456......16629.......118863.........863435

.1..10...136...1545....16629.....184819......2076117.......23697768

.1..21...402...7154...118863....2076117.....37066859......666849212

.1..42..1180..33269...863435...23697768....666849212....18940533171

.1..86..3518.154974..6296517..272201307..12062165754...540011330454

.1.179.10525.724237.46082534.3137010024.218944306666.15442088872458

Examples

			Some solutions for n=4 k=4
..0..0..0..0....0..0..0..0....0..1..1..0....0..1..1..1....0..1..1..1
..0..1..0..0....0..0..1..0....1..1..1..1....1..1..1..1....1..1..1..1
..0..0..1..1....0..0..0..0....1..1..0..1....1..1..1..1....1..1..1..0
..0..0..1..1....0..0..0..0....0..1..1..1....0..1..1..0....1..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 2 is A240513(n-2)

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

k=3: [order 15]

k=4: [order 50]