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A356915
Number of partitions of n into 4 parts that divide n.
0
0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 7, 0, 0, 0, 2, 0, 3, 0, 3, 0, 0, 0, 9, 0, 0, 0, 1, 0, 4, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 3, 0, 1, 0, 0, 0, 9, 0, 1, 0, 1, 0, 3, 0, 2, 0, 0, 0, 10, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 10, 0, 0, 0, 1, 0, 2, 0, 4, 0, 0, 0, 8, 0, 0, 0, 2, 0, 5
OFFSET
1,6
FORMULA
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} c(n/k) * c(n/j) * c(n/i) * c(n/(n-i-j-k)), where c(n) = 1 - ceiling(n) + floor(n).
EXAMPLE
a(12) = 7; there are 7 ways to write 12 as the sum of 4 divisors of 12: 6+4+1+1 = 6+3+2+1 = 6+2+2+2 = 4+4+3+1 = 4+4+2+2 = 4+3+3+2 = 3+3+3+3.
CROSSREFS
Cf. A354591.
Sequence in context: A328766 A219203 A341981 * A226786 A266330 A320313
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Sep 04 2022
STATUS
approved