A350937
Minimal permanent of an n X n Toeplitz matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 7, 89, 2287, 89025, 5141775, 404316249
Offset: 0
a(2) = 7:
1 2
3 1
a(3) = 89:
1 2 4
3 1 2
5 3 1
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from itertools import permutations
from sympy import Matrix
def A350937(n): return 1 if n == 0 else min(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
A351020
Maximal permanent of an n X n symmetric Toeplitz matrix using the integers 1 to n.
Original entry on oeis.org
1, 1, 5, 64, 1650, 66731, 3968777, 323676148, 34890266414, 4780256317586, 814873637329516, 168491370685328792
Offset: 0
a(3) = 64:
2 3 1
3 2 3
1 3 2
a(4) = 1650:
3 4 2 1
4 3 4 2
2 4 3 4
1 2 4 3
a(5) = 66731:
3 5 4 2 1
5 3 5 4 2
4 5 3 5 4
2 4 5 3 5
1 2 4 5 3
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from itertools import permutations
from sympy import Matrix
def A351020(n): return 1 if n == 0 else max(Matrix([p[i:0:-1]+p[0:n-i] for i in range(n)]).per() for p in permutations(range(1,n+1))) # Chai Wah Wu, Jan 31 2022
A358570
a(n) is the maximal permanent of an n X n Toeplitz matrix using the integers 0 to 2*(n - 1).
Original entry on oeis.org
1, 0, 4, 121, 6109, 494610, 58369622
Offset: 0
a(2) = 4:
[2, 0;
1, 2]
a(3) = 121:
[4, 2, 1;
3, 4, 2;
0, 3, 4]
A350940
Maximal permanent of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
Original entry on oeis.org
1, 2, 31, 2364, 346018, 82285908, 39135296624
Offset: 0
a(2) = 31:
5 2
3 5
a(3) = 2364:
11 5 3
7 11 5
2 7 11
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a[n_] := Max[Table[Permanent[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 = matpermanent(matrix(n, n, i, j, prime(p[i+j-1]))); if (d>m, m = d)); m; \\ Michel Marcus, Feb 08 2024
-
from itertools import permutations
from sympy import Matrix, prime
def A350940(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(prime(i) for i in range(1,2*n))) # Chai Wah Wu, Jan 27 2022
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.
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.
A351611
Maximal permanent of an n X n symmetric matrix using the integers 1 to n*(n + 1)/2.
Original entry on oeis.org
1, 1, 11, 420, 41451, 7985639, 2779152652
Offset: 0
a(3) = 420:
1 5 6
5 3 4
6 4 2
a(4) = 41451:
1 5 8 10
5 4 9 7
8 9 3 6
10 7 6 2
A369943
a(n) is the number of distinct values of the permanent of an n X n Hankel matrix using the integers 1 to 2*n - 1.
Original entry on oeis.org
1, 1, 2, 49, 2117, 156189, 16943487
Offset: 0
-
a[n_] := CountDistinct[Table[Permanent[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, matpermanent(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 A369943(n): return len({Matrix([p[i:i+n] for i in range(n)]).per() for p in permutations(range(1,n<<1))}) # Chai Wah Wu, Feb 12 2024
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