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A323255
The permanent of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 2*n - 1, n - 1, ..., 1 and whose first column consists of 2*n - 1, 2*n - 2, ..., n.
2
1, 1, 11, 248, 9968, 638772, 60061657, 7798036000, 1336715859150, 292406145227392, 79483340339739367, 26280500564448081664, 10386012861097225139356, 4834639222955142417477888, 2618110215141486526589786501, 1631888040186649673361825042432, 1159983453675106278249250918734938
OFFSET
0,3
COMMENTS
The trace of the matrix M(n) is A000384(n).
The sum of the first row of the matrix M(n) is A034856(n).
The sum of the first column of the matrix M(n) is A000326(n).
For n > 1, the sum of the superdiagonal of the matrix M(n) is A000290(n-1).
For n > 1, the sum of the subdiagonal of the matrix M(n) is A001105(n-1).
LINKS
Wikipedia, Toeplitz matrix
EXAMPLE
For n = 1 the matrix M(1) is
1
with permanent a(1) = 1.
For n = 2 the matrix M(2) is
3, 1
2, 3
with permanent a(2) = 11.
For n = 3 the matrix M(3) is
5, 2, 1
4, 5, 2
3, 4, 5
with permanent a(3) = 248.
MATHEMATICA
b[i_]:=i; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Join[{b[2*n-1]}, Array[b, n-1, {2*n-2, n }]], Join[{b[2*n-1]}, Array[b, n-1, {n-1, 1}]]]]]; Array[a, 16, 0]
PROG
(PARI) tm(n) = {my(m = matrix(n, n, i, j, if (j==1, 2*n-i, n-j+1))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }
a(n) = matpermanent(tm(n)); \\ Stefano Spezia, Dec 11 2019
CROSSREFS
Cf. A323254 (determinant of matrix M(n)).
Sequence in context: A243683 A377495 A377494 * A167868 A368190 A377328
KEYWORD
nonn
AUTHOR
Stefano Spezia, Jan 09 2019
EXTENSIONS
a(0) = 1 prepended by Stefano Spezia, Dec 08 2019
STATUS
approved