A295416 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

1, 2, 2, 4, 10, 4, 7, 36, 36, 7, 12, 126, 234, 126, 12, 21, 454, 1534, 1534, 454, 21, 37, 1632, 10291, 19026, 10291, 1632, 37, 65, 5854, 68613, 240439, 240439, 68613, 5854, 65, 114, 21010, 457178, 3019079, 5741797, 3019079, 457178, 21010, 114, 200, 75412

Offset

1,2

Comments

Table starts

...1.....2........4..........7............12..............21.................37

...2....10.......36........126...........454............1632...............5854

...4....36......234.......1534.........10291...........68613.............457178

...7...126.....1534......19026........240439.........3019079...........37927609

..12...454....10291.....240439.......5741797.......136204120.........3232240913

..21..1632....68613....3019079.....136204120......6093564449.......272714953724

..37..5854...457178...37927609....3232240913....272714953724.....23025368248778

..65.21010..3048314..476686533...76727059034..12210363190599...1945003010538968

.114.75412.20323497.5990217198.1821136011730.546643613178667.164274708080518128

Links

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

Formula

Empirical for column k:

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

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

k=3: a(n) = 6*a(n-1) +28*a(n-3) +3*a(n-4) +49*a(n-5) +33*a(n-6) -34*a(n-7) -22*a(n-8)

k=4: [order 14]

k=5: [order 37]

k=6: [order 78]

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..0. .0..0..1..1
..1..0..1..1. .0..0..1..0. .0..1..1..1. .0..1..0..0. .1..1..1..1
..1..1..1..0. .1..1..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..1
..0..1..0..0. .1..0..0..1. .1..1..0..1. .1..1..0..1. .0..0..1..1
..0..0..1..1. .0..0..1..1. .1..1..1..1. .1..1..1..0. .0..1..1..1

Crossrefs

Column 1 is A005251(n+2).

Column 2 is A202796.

Sequence in context: A295531 A220259 A220323 * A202802 A059473 A240629

Adjacent sequences: A295413 A295414 A295415 * A295417 A295418 A295419

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 22 2017

Status

approved