A183897 Number of nondecreasing arrangements of n+3 numbers in 0..2 with each number being the sum mod 3 of three others.

1, 7, 17, 25, 34, 44, 55, 67, 80, 94, 109, 125, 142, 160, 179, 199, 220, 242, 265, 289, 314, 340, 367, 395, 424, 454, 485, 517, 550, 584, 619, 655, 692, 730, 769, 809, 850, 892, 935, 979, 1024, 1070, 1117, 1165, 1214, 1264, 1315, 1367, 1420, 1474, 1529, 1585, 1642

Offset: 1

Author

R. H. Hardin, Jan 07 2011

Keywords

• nonn

Comments

Column 2 of A183904.

Examples

			Some solutions for n=4:
..0....0....0....0....1....0....0....0....1....0....0....0....0....0....0....0
..1....1....0....0....1....0....0....0....1....0....0....0....0....0....1....0
..1....1....2....0....1....0....1....0....1....0....1....0....0....1....1....1
..2....1....2....0....2....1....1....0....1....1....1....0....0....1....1....1
..2....1....2....1....2....1....1....2....2....2....2....0....1....1....1....1
..2....2....2....1....2....1....1....2....2....2....2....1....2....1....1....2
..2....2....2....1....2....1....1....2....2....2....2....1....2....2....2....2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..62
• Charles Cratty, Samuel Erickson, Frehiwet Negass, Lara Pudwell, Pattern Avoidance in Double Lists, preprint, 2015.

Crossrefs

Cf. A183904.

Formula

Empirical: a(n) = (1/2)*n^2 + (9/2)*n - 1 for n>2.

Conjectures from Colin Barker, Apr 05 2018: (Start)

G.f.: x*(1 + x - x^2)*(1 + 3*x - 3*x^2) / (1 - x)^3.

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

(End)