A266429 Number of 3 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.

4, 13, 39, 106, 259, 574, 1170, 2223, 3982, 6787, 11089, 17472, 26677, 39628, 57460, 81549, 113544, 155401, 209419, 278278, 365079, 473386, 607270, 771355, 970866, 1211679, 1500373, 1844284, 2251561, 2731224, 3293224, 3948505, 4709068, 5588037

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/360)*n^6 + (1/40)*n^5 + (1/9)*n^4 + (7/24)*n^3 + (319/360)*n^2 + (101/60)*n + 1.

Conjectures from Colin Barker, Jan 09 2019: (Start)

G.f.: x*(4 - 15*x + 32*x^2 - 34*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 3 of A266428.

Sequence in context: A027076 A183112 A364647 * A105693 A215404 A290929

Adjacent sequences: A266426 A266427 A266428 * A266430 A266431 A266432

Keyword

nonn

Author

R. H. Hardin, Dec 29 2015

Status

approved