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

Author

R. H. Hardin, Jun 29 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

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)

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)