A227637 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order.

2, 5, 11, 23, 44, 78, 130, 206, 313, 459, 653, 905, 1226, 1628, 2124, 2728, 3455, 4321, 5343, 6539, 7928, 9530, 11366, 13458, 15829, 18503, 21505, 24861, 28598, 32744, 37328, 42380, 47931, 54013, 60659, 67903, 75780, 84326, 93578, 103574, 114353

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Conjectures from Colin Barker, Sep 09 2018: (Start)

G.f.: x*(2 - 5*x + 6*x^2 - 2*x^3 - x^4 + x^5) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Column 2 of A227641.

Sequence in context: A281969 A124920 A064934 * A171985 A354044 A005986

Adjacent sequences: A227634 A227635 A227636 * A227638 A227639 A227640

Keyword

nonn

Author

R. H. Hardin, Jul 18 2013

Status

approved