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

1,5

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

Links

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

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]

Example

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

Crossrefs

Column 2 is A240513(n-2)

Sequence in context: A174446 A071201 A318045 * A106476 A101566 A331447

Adjacent sequences: A240653 A240654 A240655 * A240657 A240658 A240659

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 09 2014

Status

approved