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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 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 22:55 EDT 2019. Contains 328244 sequences. (Running on oeis4.)