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A295847 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s. 8
1, 2, 2, 4, 11, 4, 7, 29, 29, 7, 12, 80, 104, 80, 12, 21, 261, 467, 467, 261, 21, 37, 789, 2197, 3472, 2197, 789, 37, 65, 2354, 9645, 26544, 26544, 9645, 2354, 65, 114, 7199, 43335, 190943, 333366, 190943, 43335, 7199, 114, 200, 21889, 195508, 1406191 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

...2....11.....29.......80........261..........789...........2354

...4....29....104......467.......2197.........9645..........43335

...7....80....467.....3472......26544.......190943........1406191

..12...261...2197....26544.....333366......3804661.......45214991

..21...789...9645...190943....3804661.....68406015.....1296880337

..37..2354..43335..1406191...45214991...1296880337....39611268638

..65..7199.195508.10368395..538013975..24467737897..1200659717965

.114.21889.876170.76065766.6343699611.457692634063.36061398110075

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..311

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) +6*a(n-3) -8*a(n-4)

k=3: [order 9]

k=4: [order 16]

k=5: [order 35]

k=6: [order 73]

EXAMPLE

Some solutions for n=4 k=4

..1..0..0..0. .1..1..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0

..1..0..1..1. .0..0..0..0. .1..0..0..1. .1..0..0..0. .1..0..0..1

..1..0..1..0. .1..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..0

..1..0..0..0. .0..0..0..1. .0..0..1..0. .1..0..1..1. .0..1..0..0

CROSSREFS

Column 1 is A005251(n+2).

Sequence in context: A196856 A196707 A196950 * A296739 A218823 A296599

Adjacent sequences:  A295844 A295845 A295846 * A295848 A295849 A295850

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 29 2017

STATUS

approved

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Last modified January 23 20:47 EST 2022. Contains 350515 sequences. (Running on oeis4.)