OFFSET
0,3
COMMENTS
A(n) is an n X n matrix whose elements start from 1 at the corners and get higher, the more they are at the center (see the examples).
det(A(1)) = 1 and det(A(n)) = 0 for n > 1.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..36
FORMULA
a(2*n) = A349108(2*n).
EXAMPLE
For n = 5 the matrix A(5) is
1, 2, 3, 2, 1
2, 3, 4, 3, 2
3, 4, 5, 4, 3
2, 3, 4, 3, 2
1, 2, 3, 2, 1
with permanent a(5) = 9084.
For n = 6 the matrix A(6) is
1, 2, 3, 3, 2, 1
2, 3, 4, 4, 3, 2
3, 4, 5, 5, 4, 3
3, 4, 5, 5, 4, 3
2, 3, 4, 4, 3, 2
1, 2, 3, 3, 2, 1
with permanent a(6) = 314736.
MATHEMATICA
A[i_, j_, n_] := n - Abs[(n + 1)/2 - i] - Abs[(n + 1)/2 - j]; a[n_]:=Permanent[Table[A[i, j, n], {i, n}, {j, n}]]; Array[a, 18]
PROG
(PARI) a(n) = matpermanent(matrix(n, n, i, j, n - abs((n + 1)/2 - i) - abs((n + 1)/2 - j))); \\ Michel Marcus, Nov 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 08 2021
STATUS
approved