|
|
A370357
|
|
Number of partitions of [3n] into n sets of size 3 avoiding any set {3j-2,3j-1,3j} (1<=j<=n).
|
|
4
|
|
|
1, 0, 9, 252, 14337, 1327104, 182407545, 34906943196, 8877242235393, 2896378850249568, 1179516253790272041, 586470881874514605660, 349649630741370155550849, 246214807676005971547223712, 202182156277565590613022234777, 191496746966087534845272710637564
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{j=0..n} (-1)^(n-j) * binomial(n,j) * A025035(j).
|
|
EXAMPLE
|
a(0) = 1: the empty partition satisfies the condition.
a(1) = 0: 123 is not counted.
a(2) = 9: 124|356, 125|346, 126|345, 134|256, 135|246, 136|245, 145|236, 146|235, 156|234 are counted. 123|456 is not counted.
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n<3, [1, 0, 9][n+1],
9*(n*(n-1)/2*a(n-1)+(n-1)^2*a(n-2)+(n-1)*(n-2)/2*a(n-3)))
end:
seq(a(n), n=0..20);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|