OFFSET
0,4
COMMENTS
Conjectures (confirmed up to n = 10): (Start)
a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal. (End)
LINKS
Wikipedia, Toeplitz Matrix.
FORMULA
a(0) = 1, a(4) = 5, and a(n) = (n-1)! for n > 0 and n <> 4.
a(n) = (n - 1)*a(n-1) for n > 5.
MATHEMATICA
nmax=24; CoefficientList[Series[1-x^4/24-Log[1-x], {x, 0, nmax}], x]*Range[0, nmax]!
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Jul 14 2024
STATUS
approved