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A296688 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s. 8
1, 2, 2, 4, 12, 4, 7, 43, 43, 7, 12, 145, 210, 145, 12, 21, 524, 1162, 1162, 524, 21, 37, 1888, 6959, 11478, 6959, 1888, 37, 65, 6737, 39608, 121477, 121477, 39608, 6737, 65, 114, 24093, 226599, 1210458, 2323514, 1210458, 226599, 24093, 114, 200, 86250 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1.....2.......4..........7...........12.............21...............37
...2....12......43........145..........524...........1888.............6737
...4....43.....210.......1162.........6959..........39608...........226599
...7...145....1162......11478.......121477........1210458.........12227803
..12...524....6959.....121477......2323514.......40828110........732185986
..21..1888...39608....1210458.....40828110.....1231267842......38342595769
..37..6737..226599...12227803....732185986....38342595769....2094245366560
..65.24093.1305725..124103052..13222385649..1202783176853..115207878553368
.114.86250.7497482.1254382781.237236541596.37385385800350.6267132000869767
LINKS
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) +11*a(n-3) -2*a(n-4) +8*a(n-5) -4*a(n-6)
k=3: [order 12]
k=4: [order 26]
k=5: [order 63]
EXAMPLE
Some solutions for n=4 k=4
..1..0..1..1. .0..1..1..0. .1..0..0..0. .0..0..1..1. .0..0..1..0
..0..1..0..1. .0..1..0..1. .1..0..0..0. .1..0..0..0. .0..0..0..1
..0..0..1..0. .1..0..0..1. .0..0..0..0. .0..1..0..0. .0..1..0..0
..0..0..1..0. .0..0..0..1. .0..0..1..1. .0..1..1..1. .1..1..1..0
CROSSREFS
Column 1 is A005251(n+2).
Sequence in context: A260878 A064880 A115011 * A219569 A202795 A256890
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 18 2017
STATUS
approved

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Last modified April 17 05:47 EDT 2024. Contains 371756 sequences. (Running on oeis4.)