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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 7
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 (list; table; graph; refs; listen; history; text; internal format)
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 A176653

Adjacent sequences:  A240653 A240654 A240655 * A240657 A240658 A240659

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 09 2014

STATUS

approved

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Last modified October 17 01:24 EDT 2018. Contains 316275 sequences. (Running on oeis4.)