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

1,2

Comments

Column 2 of A183904.

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.

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)

Example

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

Crossrefs

Cf. A183904.

Sequence in context: A263264 A072199 A309231 * A300186 A355680 A354672

Adjacent sequences: A183894 A183895 A183896 * A183898 A183899 A183900

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved