A034921 Number of different determinants of n X n persymmetric matrices with entries {-1,0,+1}.

3, 4, 9, 23, 67, 192, 833, 2857, 13797, 53336, 302115, 1271704

Offset

1,1

Comments

A persymmetric (or Hankel) matrix has M[ i,j ] = M[ i-k,j+k ] for all i and j (matrix is constant along antidiagonals).

Links

Table of n, a(n) for n=1..12.

Example

For n = 1 and 2 the possible values for the determinant are {-1, 0, 1} and {-2, -1, 0, 1}.

Mathematica

M[row_] := With[{m=Length[row]}, Table[RotateLeft[row, n][[1 ;; (m+1)/2]], {n, 0, (m-1)/2}]];
a[n_] := Det[M[#]]& /@ Tuples[{-1, 0, 1}, 2n-1] // Union // Length;
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 6}] (* Jean-François Alcover, Sep 04 2017 *)

Crossrefs

Cf. A034917, A034918, A034919, A034920.

Sequence in context: A299123 A245455 A296265 * A038222 A038629 A354545

Adjacent sequences: A034918 A034919 A034920 * A034922 A034923 A034924

Keyword

nonn,nice,more

Author

Fred Lunnon, Dec 11 1999

Extensions

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 08 2006

a(10)-a(12) from Bert Dobbelaere, Jan 26 2019

Status

approved