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

1,1

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

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

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

Adjacent sequences: A217836 A217837 A217838 * A217840 A217841 A217842

Keyword

nonn,tabl

Author

R. H. Hardin Oct 12 2012

Status

approved