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URL: https://oeis.org/A183782

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A183782
T(n,k) = half the number of (n+1) X (k+1) binary arrays with no 2 X 2 subblock having exactly 2 ones.
10
5, 13, 13, 33, 47, 33, 85, 161, 161, 85, 217, 567, 730, 567, 217, 557, 1969, 3435, 3435, 1969, 557, 1425, 6887, 15887, 21935, 15887, 6887, 1425, 3653, 24001, 74148, 136843, 136843, 74148, 24001, 3653, 9353, 83799, 344483, 864671, 1146964, 864671, 344483
OFFSET
1,1
COMMENTS
All columns (or rows) are linear recurrences with constant coefficients with the order of the recurrence <= A005418(k+1). For columns up to k=6, the only case where the order is strictly less than this upper bound is for column 4. - Andrew Howroyd, Jan 09 2025
LINKS
EXAMPLE
Table starts:
5 13 33 85 217 557 1425
13 47 161 567 1969 6887 24001
33 161 730 3435 15887 74148 344483
85 567 3435 21935 136843 864671 5431499
217 1969 15887 136843 1146964 9764363 82573675
557 6887 74148 864671 9764363 112439612 1284649009
1425 24001 344483 5431499 82573675 1284649009 19815396763
3653 83799 1604473 34228999 701022093 14750484447 307446383061
9353 292305 7462786 215374371 5941108591 169027656900 4760294305144
23965 1020103 34738575 1356329167 50402814448 1939448495087 73819487702999
...
Some solutions with a(1,1)=0 for 4 X 3:
..0..0..1....0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..1..1
..1..0..0....0..0..0....0..1..0....0..0..0....0..1..1....0..0..0....1..1..1
..0..0..1....1..0..1....1..1..1....1..0..1....1..1..0....0..0..0....0..1..1
..0..0..0....0..0..0....1..1..1....1..1..1....1..0..0....0..1..0....0..0..1
CROSSREFS
Main diagonal is A183773.
Cf. A005418.
Sequence in context: A386520 A321992 A231806 * A341751 A244435 A134202
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 07 2011
STATUS
approved