|
|
A165738
|
|
Rank deficiency (= dimension of the null space) of the n X n "Lights Out" puzzle on a torus.
|
|
3
|
|
|
0, 0, 4, 0, 8, 8, 0, 0, 4, 16, 0, 16, 0, 0, 12, 0, 16, 8, 0, 32, 4, 0, 0, 32, 8, 0, 4, 0, 0, 24, 40, 0, 44, 32, 8, 16, 0, 0, 4, 64, 0, 8, 0, 0, 12, 0, 0, 64, 0, 16, 20, 0, 0, 8, 8, 0, 4, 0, 0, 48, 0, 80, 52, 0, 56, 88, 0, 64, 4, 16, 0, 32, 0, 0, 12, 0, 0, 8, 0, 128, 4, 0, 0, 16, 24, 0, 4, 0, 0, 24
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
The number of solutions to the puzzle is 2^a(n). If a(n)=0 then the puzzle has a unique solution.
|
|
REFERENCES
|
See A075462 for further references.
|
|
LINKS
|
|
|
FORMULA
|
a(n) <= 2n.
a(n) is a multiple of 4 and satisfies a(2n) = 2a(n). a(n+1) = 2 * A159257(n) + 4 if n = 2 (mod 3) and a(n+1) = 2 * A159257(n) otherwise. - Thomas Buchholz, May 22 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|