|
|
A253155
|
|
Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
|
|
1
|
|
|
109, 120, 129, 164, 236, 380, 668, 1244, 2396, 4700, 9308, 18524, 36956, 73820, 147548, 295004, 589916, 1179740, 2359388, 4718684, 9437276, 18874460, 37748828, 75497564, 150995036, 301989980, 603979868, 1207959644, 2415919196, 4831838300
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 3*a(n-1) - 2*a(n-2) for n>5.
Empirical: a(n) = 9*2^(n-1) + 92 for n>3.
Empirical g.f.: x*(109 - 207*x - 13*x^2 + 17*x^3 + 2*x^4) / ((1 - x)*(1 - 2*x)). - Colin Barker, Dec 09 2018
|
|
EXAMPLE
|
Some solutions for n=6:
..0..1..1..1..1....0..0..0..0..0....1..0..0..0..1....0..0..0..1..0
..0..0..0..0..0....1..1..1..1..1....1..0..0..0..1....1..0..0..1..0
..1..1..1..1..1....1..1..1..1..1....1..0..0..0..1....1..0..0..1..0
..1..1..1..1..1....1..1..1..1..1....1..0..0..0..1....1..0..0..1..0
..0..0..0..0..0....0..0..0..0..0....1..0..0..0..1....1..0..0..1..0
..0..0..0..0..0....1..1..1..1..1....1..0..0..0..1....1..0..0..1..0
..0..0..0..0..1....0..0..0..0..0....1..0..0..0..1....1..0..0..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|