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A217839
T(n,k)=Number of n element 0..1 arrays with each element the minimum of k adjacent elements of a random 0..1 array of n+k-1 elements
2
2, 2, 4, 2, 4, 8, 2, 4, 7, 16, 2, 4, 7, 12, 32, 2, 4, 7, 11, 21, 64, 2, 4, 7, 11, 17, 37, 128, 2, 4, 7, 11, 16, 27, 65, 256, 2, 4, 7, 11, 16, 23, 44, 114, 512, 2, 4, 7, 11, 16, 22, 34, 72, 200, 1024, 2, 4, 7, 11, 16, 22, 30, 52, 117, 351, 2048, 2, 4, 7, 11, 16, 22, 29, 42, 81, 189, 616
OFFSET
1,1
COMMENTS
Table starts
.....2....2....2....2...2...2...2...2...2...2...2...2...2...2
.....4....4....4....4...4...4...4...4...4...4...4...4...4...4
.....8....7....7....7...7...7...7...7...7...7...7...7...7...7
....16...12...11...11..11..11..11..11..11..11..11..11..11..11
....32...21...17...16..16..16..16..16..16..16..16..16..16..16
....64...37...27...23..22..22..22..22..22..22..22..22..22..22
...128...65...44...34..30..29..29..29..29..29..29..29..29..29
...256..114...72...52..42..38..37..37..37..37..37..37..37..37
...512..200..117...81..61..51..47..46..46..46..46..46..46..46
..1024..351..189..126..91..71..61..57..56..56..56..56..56..56
..2048..616..305..194.137.102..82..72..68..67..67..67..67..67
..4096.1081..493..296.205.149.114..94..84..80..79..79..79..79
..8192.1897..798..450.303.218.162.127.107..97..93..92..92..92
.16384.3329.1292..685.443.316.232.176.141.121.111.107.106.106
.32768.5842.2091.1046.644.452.331.247.191.156.136.126.122.121
LINKS
FORMULA
Empirical for columns 1-7: a(n) = 2*a(n-1) -a(n-2) +a(n-k-1)
EXAMPLE
Some solutions for n=8 k=4
..0....0....1....0....1....0....1....1....0....1....0....0....0....0....0....0
..1....1....1....1....0....0....1....1....1....0....0....1....0....1....0....0
..1....1....1....1....0....1....0....1....1....0....1....0....1....0....0....0
..1....1....0....0....0....0....0....0....0....0....1....0....1....0....1....0
..1....1....0....0....0....0....0....0....0....0....1....0....1....0....1....1
..1....1....0....0....0....0....0....0....0....1....1....0....1....0....1....0
..1....0....0....0....0....0....0....0....0....1....1....0....0....1....1....0
..0....0....1....0....1....0....1....0....1....1....1....1....0....1....0....0
CROSSREFS
Column 2 is A005251(n+3)
Column 3 is A005252(n+3)
Column 4 is A005253(n+3)
Column 5 is A005689(n+6)
Column 6 is A098574(n+6)
Diagonal is A000124
Sequence in context: A219451 A097800 A183402 * A083779 A045865 A319862
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Oct 12 2012
STATUS
approved