|
|
A266465
|
|
Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
|
|
1
|
|
|
2, 5, 12, 29, 67, 147, 303, 590, 1090, 1922, 3253, 5311, 8400, 12918, 19377, 28425, 40873, 57722, 80196, 109776, 148240, 197703, 260666, 340063, 439318, 562401, 713894, 899055, 1123895, 1395251, 1720873, 2109508, 2570998, 3116374, 3757967
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 5*a(n-1) - 8*a(n-2) + a(n-3) + 9*a(n-4) - 6*a(n-5) - 6*a(n-7) + 9*a(n-8) + a(n-9) - 8*a(n-10) + 5*a(n-11) - a(n-12).
Empirical g.f.: x*(2 - 5*x + 3*x^2 + 7*x^3 - 5*x^4 - x^5 - 3*x^6 + 7*x^7 - 7*x^9 + 5*x^10 - x^11) / ((1 - x)^8*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jan 10 2019
|
|
EXAMPLE
|
Some solutions for n=4:
..0..0..0....0..0..0....0..1..1....0..1..1....0..0..1....0..0..1....0..0..1
..0..0..0....0..1..1....1..0..1....1..0..1....0..1..0....1..1..0....0..1..0
..0..0..0....1..0..0....1..1..0....1..1..0....1..0..0....1..1..1....1..0..0
..0..0..0....1..1..1....1..1..0....1..1..1....1..1..0....1..1..1....1..1..1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|