|
|
A201533
|
|
Number of n X 2 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
|
|
1
|
|
|
3, 9, 25, 69, 175, 410, 899, 1859, 3649, 6840, 12311, 21378, 35964, 58819, 93800, 146222, 223292, 334639, 492954, 714755, 1021293, 1439616, 2003809, 2756429, 3750155, 5049674, 6733825, 8898024, 11656994, 15147825, 19533390, 25006144
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/40320)*n^8 - (1/3360)*n^7 + (23/2880)*n^6 - (1/48)*n^5 + (247/5760)*n^4 + (231/160)*n^3 - (6777/1120)*n^2 + (3121/168)*n - 20 for n>3.
G.f.: x*(3 - 18*x + 52*x^2 - 84*x^3 + 76*x^4 - 25*x^5 - 19*x^6 + 20*x^7 + x^8 - 9*x^9 + 5*x^10 - x^11) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>12.
(End)
|
|
EXAMPLE
|
Some solutions for n=10:
..0..2....0..2....0..1....0..0....0..1....0..2....0..0....0..0....0..1....0..1
..0..2....0..2....0..1....0..1....0..1....0..2....0..0....0..1....0..1....0..1
..0..2....0..2....1..1....1..1....0..1....2..0....0..0....0..1....0..1....0..1
..0..2....0..2....1..2....1..1....0..1....2..0....0..2....0..2....1..0....0..1
..0..2....0..2....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
..1..1....1..0....1..2....1..2....1..0....2..0....1..2....0..2....1..0....1..0
..1..1....1..0....1..2....2..1....1..0....2..2....2..2....0..2....1..1....2..2
..1..2....2..0....2..0....2..1....2..1....2..2....2..2....2..1....2..1....2..2
..1..2....2..0....2..0....2..2....2..1....2..2....2..2....2..1....2..2....2..2
..1..2....2..2....2..2....2..2....2..2....2..2....2..2....2..1....2..2....2..2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|