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]
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]
A374342
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 first n-1 primes off-diagonal.
Original entry on oeis.org
1, 1, 3, 15, 259, 12167, 1708047, 157042600, 33081320935, 3336975844504, 579469550006151
Offset: 0
a(5) = 12167:
[1, 2, 7, 3, 5]
[2, 1, 2, 7, 3]
[7, 2, 1, 2, 7]
[3, 7, 2, 1, 2]
[5, 3, 7, 2, 1]
-
a[n_]:=Max[Table[Abs[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Prime[Range[n-1]]],i]]]]],{i,(n-1)!}]]; Join[{1},Array[a,10]]
A374617
a(n) is the number of distinct values 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, 1, 2, 6, 21, 111, 710, 4968, 39879, 360952
Offset: 0
-
a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{1},Part[Permutations[Range[n-1]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]
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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