A184540 Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

45, 89, 147, 220, 309, 415, 539, 682, 845, 1029, 1235, 1464, 1717, 1995, 2299, 2630, 2989, 3377, 3795, 4244, 4725, 5239, 5787, 6370, 6989, 7645, 8339, 9072, 9845, 10659, 11515, 12414, 13357, 14345, 15379, 16460, 17589, 18767, 19995, 21274, 22605, 23989

Offset

1,1

Comments

Column 1 of A184548.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = (84 + 149*n + 36*n^2 + n^3) / 6. Corrected by Colin Barker, Apr 12 2018~

Conjectures from Colin Barker, Apr 12 2018: (Start)

G.f.: x*(45 - 91*x + 61*x^2 - 14*x^3) / (1 - x)^4.

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

(End)

Example

Some solutions for 4 X 3:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..0..1....0..1..1....0..0..0....0..0..1....0..0..1....0..1..1....0..0..1
..0..1..1....0..1..1....0..0..1....1..1..1....0..1..1....0..1..1....1..1..0
..1..0..1....1..0..0....0..1..0....1..1..1....1..1..0....0..1..1....1..1..1

Crossrefs

Cf. A184548.

Sequence in context: A140380 A183625 A184548 * A115827 A070002 A101794

Adjacent sequences: A184537 A184538 A184539 * A184541 A184542 A184543

Keyword

nonn

Author

R. H. Hardin, Jan 16 2011

Status

approved