A266464 Number of n X 2 binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

1, 2, 4, 7, 12, 19, 29, 42, 59, 80, 106, 137, 174, 217, 267, 324, 389, 462, 544, 635, 736, 847, 969, 1102, 1247, 1404, 1574, 1757, 1954, 2165, 2391, 2632, 2889, 3162, 3452, 3759, 4084, 4427, 4789, 5170, 5571, 5992, 6434, 6897, 7382, 7889, 8419, 8972, 9549, 10150

Offset: 0

Author

R. H. Hardin, Dec 29 2015

Keywords

• nonn
• easy

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n=1..210 from R. H. Hardin)

Crossrefs

Column 2 of A266470.

Partial sums of A033638.

Programs

Maple

a:= proc(n) option remember;
     `if`(n<0, 0, 1+a(n-1)+floor(n^2/4))
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Dec 27 2023

Formula

a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) -a(n-5).

From Colin Barker, Mar 21 2018: (Start)

G.f.: (x^3-x+1)/((x+1)*(x-1)^4).

a(n) = (2*n^3 + 3*n^2 + 22*n + 24) / 24 for n even.

a(n) = (2*n^3 + 3*n^2 + 22*n + 21) / 24 for n odd.

(End)

Extensions

a(0)=1 prepended by Alois P. Heinz, Dec 27 2023