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, 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

Author

R. H. Hardin Oct 12 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..435

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

Formula

Empirical for columns 1-7: a(n) = 2*a(n-1) -a(n-2) +a(n-k-1)