A350954
Maximal determinant of an n X n symmetric Toeplitz matrix using the integers 1 to n.
Original entry on oeis.org
1, 1, 3, 15, 100, 3091, 49375, 1479104, 43413488, 1539619328, 64563673460, 2877312739624, 252631974548628
Offset: 0
a(3) = 15:
1 3 2
3 1 3
2 3 1
a(4) = 100:
2 1 4 3
1 2 1 4
4 1 2 1
3 4 1 2
a(5) = 3091:
3 5 1 2 4
5 3 5 1 2
1 5 3 5 1
2 1 5 3 5
4 2 1 5 3
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from itertools import permutations
from sympy import Matrix
def A350954(n): return max(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).det() for p in permutations(range(1,n+1))) # Chai Wah Wu, Jan 27 2022
A350938
Maximal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 11, 296, 14502, 1153889, 134713213, 21788125930
Offset: 0
a(2) = 11:
3 1
2 3
a(3) = 296:
5 3 2
4 5 3
1 4 5
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from itertools import permutations
from sympy import Matrix
def A350938(n): return 1 if n == 0 else max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).per() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350933
Maximal determinant of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, 19, 1115, 86087, 9603283, 2307021183, 683793949387
Offset: 0
a(2) = 19:
5 2
3 5
a(3) = 1115:
11 2 5
7 11 2
3 7 11
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a[n_] := Max[Table[Abs[Det[HankelMatrix[Join[Drop[per = Part[Permutations[Prime[Range[2 n - 1]]], i], n], {Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]] (* Stefano Spezia, Feb 06 2024 *)
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a(n) = my(v=[1..2*n-1], m=-oo, d); forperm(v, p, d = abs(matdet(matrix(n, n, i, j, prime(p[i+j-1])))); if (d>m, m = d)); m; \\ Michel Marcus, Feb 08 2024
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from itertools import permutations
from sympy import Matrix, prime
def A350933(n): return max(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(prime(i) for i in range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A350930
Minimal determinant of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, -5, -42, -1810, -48098, -2737409, -114381074
Offset: 0
a(2) = -5:
[1 2]
[3 1]
a(3) = -42:
[3 4 1]
[5 3 4]
[2 5 3]
-
from itertools import permutations
from sympy import Matrix
def A350930(n): return min(Matrix([p[n-1-i:2*n-1-i] for i in range(n)]).det() for p in permutations(range(1,2*n))) # Chai Wah Wu, Jan 27 2022
A351609
Maximal absolute value of the determinant of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.
Original entry on oeis.org
1, 1, 7, 152, 7113, 745285, 94974369
Offset: 0
a(3) = 152:
2 4 6
4 5 1
6 1 3
a(4) = 7113:
2 6 8 9
6 5 10 1
8 10 3 4
9 1 4 7
A368351
a(n) is the minimal determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, -7, -105, -1810, -48098, -3051554, -175457984
Offset: 0
a(2) = -7:
2, 3;
3, 1.
a(3) = -105:
2, 4, 5;
4, 5, 1;
5, 1, 3.
a(4) = -1810:
4, 3, 7, 1;
3, 7, 1, 2;
7, 1, 2, 5;
1, 2, 5, 6.
A358568
a(n) is the maximal determinant of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
Original entry on oeis.org
1, 0, 4, 74, 1781, 58180, 2579770, 152337045
Offset: 0
a(2) = 4:
[2, 0;
1, 2]
a(3) = 74:
[4, 0, 2;
3, 4, 0;
1, 3, 4]
A368352
a(n) is the maximal determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 5, 42, 2294, 71753, 2737409, 114381074
Offset: 0
a(2) = 5:
3, 1;
1, 2.
a(3) = 42:
2, 5, 3;
5, 3, 4;
3, 4, 1.
a(4) = 2294:
2, 3, 6, 7;
3, 6, 7, 1;
6, 7, 1, 5;
7, 1, 5, 4.
A369942
a(n) is the number of distinct values of the determinant of an n X n Hankel matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 3, 49, 1480, 50522, 2517213
Offset: 0
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a[n_] := CountDistinct[Table[Det[HankelMatrix[Join[Drop[per = Part[Permutations[Range[2 n - 1]], i], n],{Part[per, n]}], Join[{Part[per, n]}, Drop[per, - n]]]], {i, (2 n - 1) !}]]; Join[{1}, Array[a, 5]]
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a(n) = my(v=[1..2*n-1], list=List()); forperm(v, p, listput(list, matdet(matrix(n, n, i, j, p[i+j-1])));); #Set(list); \\ Michel Marcus, Feb 08 2024
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from itertools import permutations
from sympy import Matrix
def A369942(n): return len({Matrix([p[i:i+n] for i in range(n)]).det() for p in permutations(range(1,n<<1))}) # Chai Wah Wu, Feb 12 2024
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