|
|
A231126
|
|
Number of (n+1) X (3+1) white-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
|
|
2
|
|
|
6, 40, 308, 2260, 16812, 124644, 924900, 6862052, 50913012, 377747700, 2802692276, 20794524084, 154284599124, 1144711823796, 8493168927828, 63014915159220, 467538037568404, 3468890119531892, 25737368287958996, 190957944347003188
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 7*a(n-1) + 8*a(n-2) - 32*a(n-3) - 38*a(n-4) + 40*a(n-5) + 56*a(n-6) - 16*a(n-7) - 16*a(n-8).
Empirical g.f.: 2*x*(3 - x - 10*x^2 - 12*x^3 + 18*x^4 + 8*x^5 - 8*x^6) / (1 - 7*x - 8*x^2 + 32*x^3 + 38*x^4 - 40*x^5 - 56*x^6 + 16*x^7 + 16*x^8). - Colin Barker, Mar 18 2018
|
|
EXAMPLE
|
Some solutions for n=5:
..0..x..0..x....0..x..0..x....0..x..1..x....0..x..1..x....0..x..0..x
..x..1..x..2....x..1..x..2....x..2..x..0....x..2..x..2....x..1..x..0
..2..x..1..x....2..x..1..x....0..x..1..x....0..x..2..x....2..x..2..x
..x..0..x..2....x..0..x..0....x..0..x..1....x..1..x..0....x..0..x..2
..1..x..2..x....1..x..1..x....1..x..2..x....1..x..2..x....0..x..1..x
..x..2..x..1....x..0..x..0....x..1..x..1....x..2..x..1....x..2..x..2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|