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
Stefano Spezia, Table of n, a(n) for n = 0..35
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
KEYWORD
nonn
AUTHOR
Stefano Spezia, Jan 09 2019
EXTENSIONS
a(0) = 1 prepended by Stefano Spezia, Dec 08 2019
STATUS
approved