A278177 T(n,k)=Number of nXk 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.

0, 0, 0, 0, 2, 0, 0, 5, 5, 0, 0, 13, 18, 13, 0, 0, 43, 126, 126, 43, 0, 0, 137, 737, 1476, 737, 137, 0, 0, 436, 4551, 17396, 17396, 4551, 436, 0, 0, 1394, 27692, 205363, 396024, 205363, 27692, 1394, 0, 0, 4458, 169131, 2419304, 9120939, 9120939, 2419304

Offset

1,5

Comments

Table starts

.0.....0.......0..........0.............0................0...................0

.0.....2.......5.........13............43..............137.................436

.0.....5......18........126...........737.............4551...............27692

.0....13.....126.......1476.........17396...........205363.............2419304

.0....43.....737......17396........396024..........9120939...........209105063

.0...137....4551.....205363.......9120939........408355632.........18218081491

.0...436...27692....2419304.....209105063......18218081491.......1580935773900

.0..1394..169131...28515138....4797179760.....813097394374.....137264328312479

.0..4458.1032173..336046126..110034231906...36285966496008...11916307472109969

.0.14258.6300804.3960336818.2523955236624.1619341940295084.1034507705866421424

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7

k=3: [order 16] for n>18

k=4: [order 40] for n>41

Example

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

Crossrefs

Sequence in context: A223705 A358304 A285192 * A095221 A078112 A281190

Adjacent sequences: A278174 A278175 A278176 * A278178 A278179 A278180

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2016

Status

approved