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

Author

R. H. Hardin, Dec 29 2015

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 5 of A266470.

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)