A374279
a(n) is the minimal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 0, -1, 4, -44, -946, -8281, -592100, -25369920, -511563816, -55400732937
Offset: 0
a(5) = -946:
[0, 1, 4, 2, 3]
[1, 0, 1, 4, 2]
[4, 1, 0, 1, 4]
[2, 4, 1, 0, 1]
[3, 2, 4, 1, 0]
-
a[0]=1; a[n_]:=Min[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]],{i,(n-1)!}]]; Array[a,11,0]
A374280
a(n) is the maximal determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 0, -1, 8, 28, 282, 27495, 581268, 17344692, 1246207300, 33366771123
Offset: 0
a(5) = 282:
[0, 3, 4, 2, 1]
[3, 0, 3, 4, 2]
[4, 3, 0, 3, 4]
[2, 4, 3, 0, 3]
[1, 2, 4, 3, 0]
-
a[0]=1; a[n_]:=Max[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]],{i,(n-1)!}]]; Array[a,11,0]
A374282
a(n) is the minimal absolute value of the determinant of a nonsingular n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 4, 12, 2, 13, 16, 21, 4, 1
Offset: 2
a(5) = 2:
[0, 4, 1, 2, 3]
[4, 0, 4, 1, 2]
[1, 4, 0, 4, 1]
[2, 1, 4, 0, 4]
[3, 2, 1, 4, 0]
-
a[n_]:=Min[Select[Table[Abs[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]],i]]]]],{i,(n-1)!}],Positive]]; Array[a,9,2]
A374283
a(n) is the maximal permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 0, 1, 8, 256, 9978, 600052, 49036950, 5286564352, 725724599636
Offset: 0
a(5) = 9978:
[0, 4, 3, 2, 1]
[4, 0, 4, 3, 2]
[3, 4, 0, 4, 3]
[2, 3, 4, 0, 4]
[1, 2, 3, 4, 0]
-
a[0]=1; a[n_]:=Max[Table[Permanent[ToeplitzMatrix[Join[{0}, Part[Permutations[Range[n - 1]], i]]]], {i, (n-1)!}]]; Array[a, 11, 0]
A374618
a(n) is the number of distinct values of the determinant of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
Original entry on oeis.org
1, 1, 1, 2, 6, 22, 111, 695, 4920, 39881, 360242
Offset: 0
-
a[n_]:=CountDistinct[Table[Det[ToeplitzMatrix[Join[{0},Part[Permutations[Range[n-1]], i]]]], {i, (n -1)!}]]; Join[{1}, Array[a, 10]]
Showing 1-5 of 5 results.
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