A266472 Number of 5 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

6, 19, 67, 232, 735, 2090, 5371, 12645, 27639, 56726, 110334, 204903, 365538, 629531, 1050952, 1706538, 2703140, 4187021, 6355333, 9470138, 13875377, 20017232, 28468369, 39956595, 55398509, 75938776, 102995704, 138313857, 184024492

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/181440)*n^9 + (1/8064)*n^8 + (29/15120)*n^7 + (13/960)*n^6 + (301/8640)*n^5 + (101/384)*n^4 - (34619/90720)*n^3 + (37531/10080)*n^2 - (4171/2520)*n + 4.

Conjectures from Colin Barker, Jan 10 2019: (Start)

G.f.: x*(6 - 41*x + 147*x^2 - 303*x^3 + 410*x^4 - 382*x^5 + 248*x^6 - 109*x^7 + 30*x^8 - 4*x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)

Example

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

Crossrefs

Row 5 of A266470.

Sequence in context: A041673 A137195 A055916 * A259804 A060579 A183326

Adjacent sequences: A266469 A266470 A266471 * A266473 A266474 A266475

Keyword

nonn

Author

R. H. Hardin, Dec 29 2015

Status

approved