A227641 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order

1, 2, 2, 3, 5, 3, 4, 11, 11, 4, 5, 23, 39, 23, 5, 6, 44, 127, 127, 44, 6, 7, 78, 377, 667, 377, 78, 7, 8, 130, 1014, 3202, 3202, 1014, 130, 8, 9, 206, 2518, 13740, 25241, 13740, 2518, 206, 9, 10, 313, 5844, 53575, 179234, 179234, 53575, 5844, 313, 10, 11, 459, 12790

Offset

1,2

Comments

Table starts

.1...2.....3......4........5..........6............7.............8

.2...5....11.....23.......44.........78..........130...........206

.3..11....39....127......377.......1014.........2518..........5844

.4..23...127....667.....3202......13740........53575........192191

.5..44...377...3202....25241.....179234......1147095.......6679750

.6..78..1014..13740...179234....2139328.....23032705.....224466940

.7.130..2518..53575..1147095...23032705....420651813....6956310972

.8.206..5844.192191..6679750..224466940...6956310972..196026480660

.9.313.12790.640831.35730988.1995242628.104620117266.5023590617706

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = n

k=2: a(n) = (1/24)*n^4 - (1/12)*n^3 + (35/24)*n^2 - (29/12)*n + 4 for n>1

k=3: [polynomial of degree 9] for n>3

k=4: [polynomial of degree 19] for n>9

k=5: [polynomial of degree 39] for n>17

Example

Some solutions for n=4 k=4
..0..0..0..1....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..0
..0..0..0..0....0..1..0..1....0..0..0..0....0..0..0..1....0..0..0..1
..0..0..0..0....1..0..1..0....0..1..1..0....0..1..0..0....0..1..0..0
..0..1..0..0....0..0..0..0....0..0..0..0....0..0..0..0....1..0..1..0

Crossrefs

Sequence in context: A047666 A285935 A209568 * A295097 A295551 A196696

Adjacent sequences: A227638 A227639 A227640 * A227642 A227643 A227644

Keyword

nonn,tabl

Author

R. H. Hardin Jul 18 2013

Status

approved