|
|
A200890
|
|
Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors.
|
|
1
|
|
|
65, 704, 3823, 14288, 42182, 105813, 235538, 478467, 904111, 1611038, 2734601, 4455802, 7011356, 10705019, 15920244, 23134229, 32933421, 46030540, 63283187, 85714100, 114533122, 151160945, 197254694, 254735415, 325817531, 413040330
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (4/315)*n^7 + (7/9)*n^6 + (241/45)*n^5 + (1067/72)*n^4 + (3757/180)*n^3 + (1145/72)*n^2 + (2629/420)*n + 1.
G.f.: x*(65 + 184*x + 11*x^2 - 224*x^3 + 48*x^4 - 27*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
|
|
EXAMPLE
|
Some solutions for n=3
..0....2....3....2....2....3....2....0....2....0....2....2....3....2....1....1
..1....3....0....2....0....2....2....3....3....3....0....0....1....2....0....2
..1....3....0....3....3....2....1....3....3....3....3....1....2....3....2....2
..0....0....2....3....3....0....2....3....3....2....3....1....2....3....2....2
..2....1....3....0....2....0....2....2....0....3....2....0....2....3....2....2
..2....1....3....0....2....2....0....0....1....3....0....1....1....3....0....0
..2....3....2....2....1....3....1....0....3....3....1....1....0....3....1....1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|