A184544 Number of (n+2) X 7 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.

309, 792, 1627, 3024, 5313, 8989, 14767, 23648, 36997, 56634, 84939, 124972, 180609, 256695, 359215, 495484, 674357, 906460, 1204443, 1583256, 2060449, 2656497, 3395151, 4303816, 5413957, 6761534, 8387467, 10338132, 12665889, 15429643

Offset

1,1

Comments

Column 5 of A184548.

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (17/12)*n^4 + (5767/720)*n^3 + (3063/40)*n^2 + (11959/70)*n + 52.

Conjectures from Colin Barker, Apr 13 2018: (Start)

G.f.: x*(309 - 1680*x + 3943*x^2 - 5120*x^3 + 3955*x^4 - 1819*x^5 + 465*x^6 - 52*x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

Some solutions for 4 X 7:
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..1..1..1..1..1
..0..0..0..0..0..0..1....0..0..0..0..0..1..1....1..1..1..1..1..1..1
..0..0..0..0..0..1..1....0..0..1..1..1..0..0....1..1..1..1..1..1..1
..0..0..0..1..1..1..0....1..1..1..1..1..1..1....1..1..1..1..1..1..1

Crossrefs

Cf. A184548.

Sequence in context: A121322 A067730 A183627 * A251345 A105841 A127456

Adjacent sequences: A184541 A184542 A184543 * A184545 A184546 A184547

Keyword

nonn

Author

R. H. Hardin, Jan 16 2011

Status

approved