|
| |
|
|
A267905
|
|
Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
|
|
1
|
|
|
|
1, 2, 5, 13, 34, 88, 225, 569, 1426, 3548, 8777, 21613, 53026, 129712, 316545, 770993, 1874914, 4553588, 11047625, 26779909, 64869586, 157043368, 380004897, 919150313, 2222499826, 5372538572, 12984354185, 31374801373, 75801065794
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
R. H. Hardin, Table of n, a(n) for n = 1..210
|
|
|
FORMULA
|
Empirical: a(n) = 5*a(n-1) -7*a(n-2) +a(n-3) +2*a(n-4).
Conjectures from Colin Barker, Jan 11 2019: (Start)
G.f.: x*(1 - 3*x + 2*x^2 + x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)).
a(n) = ((1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n) - 2*(2^n-1)) / 4.
(End)
|
|
|
EXAMPLE
|
Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
..1....2....2....0....2....2....2....1....2....0....2....0....2....0....2....0
..2....2....2....0....1....1....1....1....0....1....0....1....1....0....0....1
..0....1....2....2....2....1....2....2....0....1....0....2....0....0....0....2
..1....0....2....0....1....1....1....1....1....1....0....0....2....2....0....1
..2....2....2....0....2....1....2....0....0....0....1....1....2....0....0....0
..1....2....2....1....1....1....2....2....2....1....0....1....2....0....2....0
|
|
|
CROSSREFS
|
Column 1 of A267911.
Sequence in context: A318234 A027931 A218481 * A209230 A103142 A112844
Adjacent sequences: A267902 A267903 A267904 * A267906 A267907 A267908
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
R. H. Hardin, Jan 22 2016
|
|
|
STATUS
|
approved
|
| |
|
|
