[seqfan] Pick some nonadjacent rows or nonadjacent columns

[Ron Hardin]

This part of a survey of clockwise-pattern tilings turned up a lot of hits of existing sequences

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

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

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

Example for n=4 m=4:
..0..0..0..0..0....0..0..1..0..0....0..0..0..0..0....0..0..0..0..0..
..0..0..0..0..0....0..0..1..0..0....0..0..0..0..0....1..1..1..1..1..
..0..0..0..0..0....0..0..1..0..0....0..0..0..0..0....0..0..0..0..0..
..1..1..1..1..1....0..0..1..0..0....0..0..0..0..0....0..0..0..0..0..
..0..0..0..0..0....0..0..1..0..0....0..0..0..0..0....1..1..1..1..1..

Column 1 is A018910\n")
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)
 rhhardin at mindspring.com
rhhardin at att.net (either)