A296599 T(n,k) = Number of n X k 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1, 2 or 3 neighboring 1's.

1, 2, 2, 4, 11, 4, 7, 39, 39, 7, 12, 136, 228, 136, 12, 21, 494, 1441, 1441, 494, 21, 37, 1785, 9194, 16524, 9194, 1785, 37, 65, 6432, 58251, 194743, 194743, 58251, 6432, 65, 114, 23201, 370000, 2271055, 4254377, 2271055, 370000, 23201, 114, 200, 83695

Offset

1,2

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) +a(n-4) +a(n-6) -a(n-7) -a(n-8)

k=3: [order 17]

k=4: [order 44]

Example

Table starts
...1.....2........4..........7...........12..............21................37
...2....11.......39........136..........494............1785..............6432
...4....39......228.......1441.........9194...........58251............370000
...7...136.....1441......16524.......194743.........2271055..........26487173
..12...494.....9194.....194743......4254377........91004329........1952733110
..21..1785....58251....2271055.....91004329......3553672817......139547279602
..37..6432...370000...26487173...1952733110....139547279602....10046940260800
..65.23201..2348956..309059200..41935988643...5483284264255...723805695940277
.114.83695.14911425.3606151826.900218672974.215325152512080.52099265384617231
...
Some solutions for n=4, k=4
..0..0..1..0. .0..1..1..0. .0..1..1..0. .0..0..0..1. .0..1..0..0
..0..1..0..0. .0..1..0..0. .1..0..0..1. .0..0..1..1. .1..0..0..0
..1..0..1..1. .0..1..0..1. .0..1..0..1. .1..1..0..0. .1..1..1..0
..1..1..0..1. .0..0..1..0. .0..1..0..1. .0..0..0..0. .0..1..1..1

Crossrefs

Column 1 is A005251(n+2).

Sequence in context: A295847 A296739 A218823 * A219106 A219985 A220800

Adjacent sequences: A296596 A296597 A296598 * A296600 A296601 A296602

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 16 2017

Status

approved