|
|
A252854
|
|
Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order.
|
|
1
|
|
|
117, 279, 684, 1719, 4383, 11286, 29241, 76059, 198324, 517923, 1353843, 3541014, 9265005, 24247215, 63465660, 166131999, 434901591, 1138526262, 2980601937, 7803157779, 20428674372, 53482546539, 140018449419, 366571967094
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) + a(n-4).
Empirical g.f.: 9*x*(13 - 21*x - 9*x^2 + 6*x^3) / ((1 - 3*x + x^2)*(1 - x - x^2)). - Colin Barker, Dec 07 2018
|
|
EXAMPLE
|
Some solutions for n=4:
..0..1..0....0..1..0....0..1..0....0..0..1....0..0..1....0..1..1....0..1..1
..1..1..0....1..2..2....1..1..0....1..0..1....1..0..1....2..0..0....0..1..0
..0..0..1....0..2..2....1..2..1....1..1..2....0..2..2....0..1..1....2..2..1
..1..0..0....0..1..1....0..1..1....2..1..2....1..2..1....0..1..1....0..2..0
..0..1..1....2..1..1....0..2..0....1..0..0....0..0..2....2..2..0....2..0..0
..1..0..0....2..0..0....2..2..0....2..0..0....0..0..1....2..2..0....2..0..2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|