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A296599 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1, 2 or 3 neighboring 1s. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 07:15 EST 2022. Contains 350573 sequences. (Running on oeis4.)