OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..452
Sela Fried, A closed form formula for A071999, 2026.
Sela Fried, Proofs of several OEIS conjectures on determinants and permanents, arXiv:2606.09913 [math.CO], 2026. See pp. 2, 10-11.
FORMULA
a(n) ~ -(-1)^(n*(n+1)/2) * ((n-2)! * (1 + (-1)^n) + (n-1)! * (1 - (-1)^n)/2). - Vaclav Kotesovec, Jan 08 2019
a(n) = Product_{i=1..floor((n-1)/2)} (1 - i*(n-i)) (see Fried link). - Sela Fried, Feb 03 2026
MAPLE
with(LinearAlgebra):
a:= n-> Determinant(Matrix(n, (i, j)->
`if`(i=j, 1, `if`(n=i+j, i, 0)))):
seq(a(n), n=0..25); # Alois P. Heinz, Nov 13 2015
MATHEMATICA
Table[ Det[ Table[ If[i == j, 1, If[n == j + i, i, 0]], {i, 1, n}, {j, 1, n}]], {n, 1, 22}]
PROG
(PARI) a(n) = matdet(matrix(n, n, i, j, if(i==j, 1, if(n==i+j, i, 0)))) \\ Colin Barker, Nov 13 2015
CROSSREFS
KEYWORD
sign
AUTHOR
Robert G. Wilson v, Jun 19 2002
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Feb 03 2026
STATUS
approved