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]
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]
A374341
a(n) is the maximal 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, 1608, 1582152, 157042600, 11778545664, 3336975844504, 440384712302421
Offset: 0
a(5) = 1608:
[1, 7, 2, 3, 5]
[7, 1, 7, 2, 3]
[2, 7, 1, 7, 2]
[3, 2, 7, 1, 7]
[5, 3, 2, 7, 1]
-
a[n_]:=Max[Table[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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