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

0,2

Links

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

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)

Example

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

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

Crossrefs

Column 2 of A266470.

Partial sums of A033638.

Sequence in context: A087149 A090853 A333311 * A103231 A002622 A363276

Adjacent sequences: A266461 A266462 A266463 * A266465 A266466 A266467

Keyword

nonn,easy

Author

R. H. Hardin, Dec 29 2015

Extensions

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

Status

approved