A227554 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having nonzero determinant, with rows and columns of the latter in lexicographically nondecreasing order.

4, 12, 33, 81, 179, 362, 680, 1201, 2014, 3232, 4995, 7473, 10869, 15422, 21410, 29153, 39016, 51412, 66805, 85713, 108711, 136434, 169580, 208913, 255266, 309544, 372727, 445873, 530121, 626694, 736902, 862145, 1003916, 1163804, 1343497

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/40)*n^5 + (17/24)*n^3 + (34/15)*n + 1.

Conjectures from Colin Barker, Sep 08 2018: (Start)

G.f.: x*(4 - 12*x + 21*x^2 - 17*x^3 + 8*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Column 2 of A227558.

Sequence in context: A168078 A225894 A318637 * A305778 A343561 A104747

Adjacent sequences: A227551 A227552 A227553 * A227555 A227556 A227557

Keyword

nonn

Author

R. H. Hardin, Jul 16 2013

Status

approved