A258316 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 or 0011

5, 7, 7, 10, 9, 10, 15, 12, 12, 15, 23, 17, 15, 17, 23, 36, 25, 20, 20, 25, 36, 57, 38, 28, 25, 28, 38, 57, 91, 59, 41, 33, 33, 41, 59, 91, 146, 93, 62, 46, 41, 46, 62, 93, 146, 235, 148, 96, 67, 54, 54, 67, 96, 148, 235, 379, 237, 151, 101, 75, 67, 75, 101, 151, 237, 379, 612

Offset

1,1

Comments

Table starts

...5...7..10..15..23..36..57..91.146.235.379.612..989.1599.2586.4183.6767.10948

...7...9..12..17..25..38..59..93.148.237.381.614..991.1601.2588.4185.6769.10950

..10..12..15..20..28..41..62..96.151.240.384.617..994.1604.2591.4188.6772.10953

..15..17..20..25..33..46..67.101.156.245.389.622..999.1609.2596.4193.6777.10958

..23..25..28..33..41..54..75.109.164.253.397.630.1007.1617.2604.4201.6785.10966

..36..38..41..46..54..67..88.122.177.266.410.643.1020.1630.2617.4214.6798.10979

..57..59..62..67..75..88.109.143.198.287.431.664.1041.1651.2638.4235.6819.11000

..91..93..96.101.109.122.143.177.232.321.465.698.1075.1685.2672.4269.6853.11034

.146.148.151.156.164.177.198.232.287.376.520.753.1130.1740.2727.4324.6908.11089

.235.237.240.245.253.266.287.321.376.465.609.842.1219.1829.2816.4413.6997.11178

Apparently: put 1s in some number of nonadjacent columns or put 1s in some number of nonadjacent rows

Links

R. H. Hardin, Table of n, a(n) for n = 1..1104

Formula

Empirical: T(n,k) = Fibonacci(n+3) +Fibonacci(k+3) -1

Empirical for rows, columns and nw-se diagonals: a(n) = 2*a(n-1) -a(n-3)

Example

Some solutions for n=4 k=4
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....1..1..1..1..1
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0

Crossrefs

Column 1 is A018910

Column 2 is A157727(n+3)

Column 3 is A187107(n+3)

Diagonal is A001595(n+2)

Superdiagonal 1 is A000071(n+5)

Superdiagonal 2 is A001610(n+3)

Superdiagonal 3 is A001595(n+4)

Superdiagonal 5 is A022308(n+5)

Superdiagonal 6 is A022319(n+5)

Superdiagonal 7 is A022407(n+5)

Superdiagonal 9 is A022323(n+7)

Sequence in context: A154475 A264527 A137755 * A244621 A201459 A053672

Adjacent sequences: A258313 A258314 A258315 * A258317 A258318 A258319

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 29 2015

Status

approved