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

1,1

Comments

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

Links

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

Example

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

Crossrefs

Sequence in context: A064464 A094585 A379837 * A295918 A296834 A242642

Adjacent sequences: A183319 A183320 A183321 * A183323 A183324 A183325

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2011

Status

approved