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A296739 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 2 or 4 king-move neighboring 1s. 8
1, 2, 2, 4, 11, 4, 7, 31, 31, 7, 12, 88, 126, 88, 12, 21, 287, 575, 575, 287, 21, 37, 881, 2832, 4251, 2832, 881, 37, 65, 2686, 13322, 34086, 34086, 13322, 2686, 65, 114, 8347, 62874, 261354, 458494, 261354, 62874, 8347, 114, 200, 25763, 299056, 2009116 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

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

...2....11......31........88.........287..........881...........2686

...4....31.....126.......575........2832........13322..........62874

...7....88.....575......4251.......34086.......261354........2009116

..12...287....2832.....34086......458494......5692727.......71592909

..21...881...13322....261354.....5692727....114153198.....2324267560

..37..2686...62874...2009116....71592909...2324267560....76925689840

..65..8347..299056..15561333...910873718..47816866681..2573555751062

.114.25763.1418177.120192735.11510112796.977475485051.85477431609556

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

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) +8*a(n-3) -12*a(n-4) +2*a(n-5) -12*a(n-6)

k=3: [order 16]

k=4: [order 35]

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A005251(n+2).

Sequence in context: A196707 A196950 A295847 * A218823 A296599 A219106

Adjacent sequences:  A296736 A296737 A296738 * A296740 A296741 A296742

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Dec 19 2017

STATUS

approved

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Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)