A183905 Number of nondecreasing arrangements of n+2 numbers in 0..2 with each number being the sum mod 3 of two others.

1, 4, 10, 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

Offset

1,2

Comments

Column 2 of A183912.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = (1/2)*n^2 + (7/2)*n - 5 for n>1.

a(n) = Triangular number(A000217)-11.

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

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)

Example

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

Mathematica

Abs[Table[n (n + 1)/2 - 11, {n, 4, 200}]] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)

Crossrefs

Cf. A000217, A183912.

Sequence in context: A246394 A310542 A366102 * A301288 A347154 A009860

Adjacent sequences: A183902 A183903 A183904 * A183906 A183907 A183908

Keyword

nonn,easy

Author

R. H. Hardin, Jan 07 2011

Status

approved