|
|
A250879
|
|
Number of (2+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
|
|
1
|
|
|
440, 1456, 3442, 6728, 11644, 18520, 27686, 39472, 54208, 72224, 93850, 119416, 149252, 183688, 223054, 267680, 317896, 374032, 436418, 505384, 581260, 664376, 755062, 853648, 960464, 1075840, 1200106, 1333592, 1476628, 1629544, 1792670
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 55*n^3 + 155*n^2 + 166*n + 64.
G.f.: 2*x*(220 - 152*x + 129*x^2 - 32*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)
|
|
EXAMPLE
|
Some solutions for n=4:
..1..1..1..1..1....2..2..2..2..0....3..3..3..3..3....2..2..2..2..2
..2..2..2..2..3....1..1..1..1..3....1..1..1..2..2....2..2..3..3..3
..1..1..1..1..3....0..0..0..1..3....0..1..1..2..3....0..1..3..3..3
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|