

A183897


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


1



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
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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(n1)  3*a(n2) + a(n3) 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 A261934 A253075
Adjacent sequences: A183894 A183895 A183896 * A183898 A183899 A183900


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 07 2011


STATUS

approved



