OFFSET
0,5
COMMENTS
A word is uniform here if each symbol that occurs in the word occurs with the same frequency.
a(n) is the number of ways to partition [n] into parts of equal size and no part containing values that differ by 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Sum_{d|n} A322013(d, n/d} for n > 0.
a(p) = 1 for prime p.
EXAMPLE
The a(4) = 2 words are abab, abcd.
The a(6) = 7 words are ababab, abacbc, abcabc, abcacb, abcbac, abcbca, abcdef.
The a(4) = 2 set partitions are {{1,3}, {2,4}} and {{1},{2},{3},{4}}.
PROG
(PARI) \\ Needs T(n, k) from A322013.
a(n) = {if(n==0, 1, sumdiv(n, d, T(d, n/d)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 06 2024
STATUS
approved