|
|
A183905
|
|
Number of nondecreasing arrangements of n+2 numbers in 0..2 with each number being the sum mod 3 of two others.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/2)*n^2 + (7/2)*n - 5 for n>1.
a(n) = Triangular number(A000217)-11.
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|