A374239
a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 1, 0, -1, 1, -545, -13805, -301184, -18551951, -352513176, -31451535983, -1209153784888, -87868166035113, -4204963833160760, -664087819207293468
Offset: 0
a(5) = -545:
[1, 1, 4, 2, 3]
[1, 1, 1, 4, 2]
[4, 1, 1, 1, 4]
[2, 4, 1, 1, 1]
[3, 2, 4, 1, 1]
-
a[0]=1; a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]
A374240
a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 1, 0, 0, 40, 256, 12232, 526773, 8684025, 768561384, 28938090375, 1273675677456, 73821863714933, 7601760995500947, 527066887623562528
Offset: 0
a(5) = 256:
[1, 4, 1, 2, 3]
[4, 1, 4, 1, 2]
[1, 4, 1, 4, 1]
[2, 1, 4, 1, 4]
[3, 2, 1, 4, 1]
-
a[0]=1; a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]
A374241
a(n) is the maximal absolute value of the determinant of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 1, 0, 1, 40, 545, 13805, 526773, 18551951, 768561384, 31451535983, 1273675677456, 87868166035113, 7601760995500947, 664087819207293468
Offset: 0
a(5) = 545:
[1, 1, 4, 2, 3]
[1, 1, 1, 4, 2]
[4, 1, 1, 1, 4]
[2, 4, 1, 1, 1]
[3, 2, 4, 1, 1]
-
a[0]=1; a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]]], {i, (n-1)!}]]; Array[a, 11, 0]
A374242
a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 1, 3, 9, 3, 1, 5, 9, 1, 1, 1, 1
Offset: 3
a(5) = 3:
[1, 1, 2, 3, 4]
[1, 1, 1, 2, 3]
[2, 1, 1, 1, 2]
[3, 2, 1, 1, 1]
[4, 3, 2, 1, 1]
-
a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]]], {i, (n-1)!}],Positive]]; Array[a, 8, 3]
A374140
a(n) is the permanent of the symmetric Toeplitz matrix of order n whose element (i,j) equals abs(i-j) or 1 if i = j.
Original entry on oeis.org
1, 1, 2, 11, 117, 2083, 55482, 2063149, 102176977, 6490667261, 514651043730, 49787897503031, 5771746960693493, 789652404867861919, 125885777192807718730, 23129357587464094132601, 4851600400570400272371009, 1152232847579194480216644249, 307579355879152834353840187554
Offset: 0
a(4) = 117:
[1, 1, 2, 3]
[1, 1, 1, 2]
[2, 1, 1, 1]
[3, 2, 1, 1]
-
a[n_]:=Permanent[Table[If[i == j, 1, Abs[i - j]], {i, n}, {j, n}]]; Join[{1}, Array[a, 18]]
-
a(n) = matpermanent(matrix(n, n, i, j, if (i==j, 1, abs(i-j)))); \\ Michel Marcus, Jun 29 2024
-
from sympy import Matrix
def A374140(n): return Matrix(n,n,[abs(j-k) if j!=k else 1 for j in range(n) for k in range(n)]).per() if n else 1 # Chai Wah Wu, Jul 01 2024
A374278
a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 1 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 1, 2, 18, 389, 14284, 798322, 62490160, 6519511313, 873036867840, 145856387327074
Offset: 0
a(5) = 14284:
[1, 4, 3, 2, 1]
[4, 1, 4, 3, 2]
[3, 4, 1, 4, 3]
[2, 3, 4, 1, 4]
[1, 2, 3, 4, 1]
-
a[0]=1; a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{1}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]
Showing 1-6 of 6 results.
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