OFFSET
0,4
COMMENTS
a(n) is the number of ordered set partitions of an n-set into 3 sets such that the first and second sets have an even number of elements, and two elements are selected from the third. "Ordered set partitions", because {}, {1,2}, {(3), (4), 5} is considered to be different from {1,2}, {}, {(3), (4), 5} .
FORMULA
a(n) = binomial(n,2)*(3^(n-2) + (-1)^n + 2)/4.
EXAMPLE
For n = 5, we have the following cases (allowing empty sets):
{}, {1,2}, {(3), (4), 5} (30 of these),
{1,2}, {}, {(3), (4), 5} (30 of these),
{}, {}, {(1), (2), 3, 4, 5} (10 of these),
where the two elements selected from the third set are in parentheses.
CROSSREFS
KEYWORD
nonn
AUTHOR
Enrique Navarrete, May 21 2024
STATUS
approved