A332566 a(n) is the permanent of an n X n symmetric Toeplitz matrix M(n) whose first row consists of a single zero followed by successive positive integers repeated (A004526).

1, 0, 1, 2, 16, 150, 2333, 45840, 1227816, 40715300, 1701223409, 84902728550, 5108474886424, 357837483830570, 29336856811970045, 2745407159100236484, 294324995624694053072, 35473014438701226021416, 4818705384665419284918401, 727012502373285844943278058, 122057159014198483893887865744

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..35

Wikipedia, Symmetric matrix

Wikipedia, Toeplitz Matrix

Example

For n = 4 the matrix M(4) is
    0 1 1 2
    1 0 1 1
    1 1 0 1
    2 1 1 0
with permanent a(4) = 16.

Mathematica

nmax:=20; k[i_]:=Floor[i/2]; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Array[k, n], Array[k, n]]]]; Table[a[n], {n, 0, nmax}]

Prog

(PARI) tm(n) = {my(m = matrix(n, n, i, j, if (i==1, floor(j/2), if (j==1, floor(i/2))))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }
a(n) = matpermanent(tm(n));

Crossrefs

Cf. A004526, A083392, A331491, A333119.

Sequence in context: A103885 A262266 A124578 * A085510 A290785 A209391

Adjacent sequences: A332563 A332564 A332565 * A332567 A332568 A332569

Keyword

nonn

Author

Stefano Spezia, Feb 16 2020

Status

approved