|
|
A255109
|
|
Number of length n+2 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
|
|
1
|
|
|
27, 75, 168, 331, 597, 1008, 1616, 2484, 3687, 5313, 7464, 10257, 13825, 18318, 23904, 30770, 39123, 49191, 61224, 75495, 92301, 111964, 134832, 161280, 191711, 226557, 266280, 311373, 362361, 419802, 484288, 556446, 636939, 726467, 825768, 935619
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (37/24)*n^3 + (175/24)*n^2 + (239/20)*n + 6.
Empirical g.f.: x*(3 - 3*x + x^2)*(9 - 20*x + 18*x^2 - 6*x^3) / (1 - x)^6. - Colin Barker, Jan 24 2018
|
|
EXAMPLE
|
Some solutions for n=4:
0 2 2 0 2 2 1 0 0 1 1 1 1 2 2 2
0 2 0 1 0 2 1 0 2 1 0 1 1 1 0 2
0 1 2 0 1 2 1 0 0 2 0 2 0 1 1 0
1 1 2 1 2 0 0 2 0 1 0 2 0 1 1 0
0 1 2 2 2 2 1 2 0 1 2 1 1 1 2 0
1 1 2 2 2 2 2 2 1 2 1 2 1 2 2 1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|