|
|
A186460
|
|
Number of (n+1) X 8 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
|
|
1
|
|
|
245, 292, 590, 945, 1681, 2377, 4121, 5633, 8893, 11977, 19037, 27133, 43249, 63485, 98801, 146333, 225061, 336241, 513933, 771609, 1174525, 1768605, 2685617, 4051469, 6143169, 9277789, 14055269, 21241521, 32162333, 48626537, 73602781
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>13.
Empirical g.f.: x*(245 - 198*x + 6*x^2 + 255*x^3 - 115*x^4 - 144*x^5 + 369*x^6 - 547*x^7 - 36*x^8 - 640*x^9 + 484*x^10 - 300*x^11 + 784*x^12) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 18 2018
|
|
EXAMPLE
|
Some solutions for 3 X 8:
..0..1..0..0..0..0..0..1....1..0..0..0..1..0..1..0....1..0..0..0..0..0..0..0
..1..0..1..0..0..0..0..0....1..0..0..0..0..1..0..1....1..0..0..0..0..0..0..0
..0..1..0..1..0..0..0..0....1..0..0..0..0..0..1..0....1..0..0..0..0..0..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|