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

Author

R. H. Hardin, Dec 29 2015

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 3 of A266428.

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)