A183322 T(n,k) is the number of n X k binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

2, 3, 3, 5, 6, 5, 8, 13, 13, 8, 13, 27, 43, 27, 13, 21, 57, 124, 124, 57, 21, 34, 119, 377, 480, 377, 119, 34, 55, 250, 1109, 1975, 1975, 1109, 250, 55, 89, 523, 3305, 7833, 11385, 7833, 3305, 523, 89, 144, 1097, 9767, 31428, 61755, 61755, 31428, 9767, 1097, 144

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn
• tabl

Comments

Empirical: column k has a 2^k order linear recurrence (verified through k=6).

Examples

			Table starts:
...2....3.....5.......8.......13.........21..........34...........55
...3....6....13......27.......57........119.........250..........523
...5...13....43.....124......377.......1109........3305.........9767
...8...27...124.....480.....1975.......7833.......31428.......125103
..13...57...377....1975....11385......61755......343035......1872913
..21..119..1109....7833....61755.....455509.....3437801.....25528515
..34..250..3305...31428...343035....3437801....35629548....360327392
..55..523..9767..125103..1872913...25528515...360327392...4963103592
..89.1097.28959..498825.10288475..190243099..3674032121..68795107993
.144.2297.85677.1985956.56225061.1412491505.37171418048.947461430557
Some solutions for 7 X 3:
..1..1..1....0..0..0....1..1..0....1..1..0....0..0..0....0..0..1....0..0..0
..1..1..1....0..0..0....1..1..1....1..1..0....1..1..1....1..1..1....0..1..1
..0..0..1....0..0..1....1..1..1....0..0..0....1..1..1....1..1..1....0..1..1
..1..1..1....0..1..1....1..1..0....1..1..0....1..1..0....0..0..1....1..1..1
..1..1..1....1..1..0....0..0..0....1..1..0....1..1..0....0..1..1....1..1..1
..0..0..1....1..1..0....0..0..1....0..1..1....1..1..0....1..1..1....0..1..1
..1..1..0....1..1..1....1..1..1....1..1..1....1..1..1....1..1..0....0..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..611