A118713 a(n) = determinant of n X n circulant matrix whose first row is A001358(1), A001358(2), ..., A001358(n) where A001358(n) = n-th semiprime.

4, -20, 361, -3567, 218053, -3455872, 736439027, -16245418225, 1519211613654, -37662452460912, 20199655476042865, -643524421698841536, 46513669467992431114, -3754367220494585505280, 277686193779526116536293, -123973821931125256333959105, 20103033234038999233385180658

Offset: 1

Author

Jonathan Vos Post, May 20 2006

Keywords

• easy
• sign

Comments

Semiprime analog of A066933 Circulant of prime numbers. a(n) alternates in sign. A048954 Wendt determinant of n-th circulant matrix C(n). A052182 Circulant of natural numbers. A086459 Circulant of powers of 2.

Examples

			a(2) = -20 = determinant
|4,6|
|6,4|.
a(3) = 361 = 19^2 = determinant
|4,6,9|
|9,4,6|
|6,9,4|.
		

Links

• Eric Weisstein's World of Mathematics, Circulant Matrix.

Crossrefs

Cf. A001358, A048954, A052182, A066933, A086459, A086569.

Programs

Maple

A118713 := proc(n)
    local C,r,c ;
    C := Matrix(1..n,1..n) ;
    for r from 1 to n do
    for c from 1 to n do
        C[r,c] := A001358(1+((c-r) mod n)) ;
    end do:
    end do:
    LinearAlgebra[Determinant](C) ;
end proc:
seq(A118713(n),n=1..13) ;

Mathematica

nmax = 13;
sp = Select[Range[3 nmax], PrimeOmega[#] == 2&];
a[n_] := Module[{M}, M[1] = sp[[1 ;; n]];
   M[k_] := M[k] = RotateRight[M[k - 1]];
   Det[Table[M[k], {k, 1, n}]]];
Table[a[n], {n, 1, nmax}] (* Jean-François Alcover, Feb 16 2023 *)

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Aug 23 2007