A118713 - OEIS

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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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Circulant Matrix.

EXAMPLE

a(2) = -20 = determinant

|4,6|

|6,4|.

a(3) = 361 = 19^2 = determinant

|4,6,9|

|9,4,6|

|6,9,4|.

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:

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 *)

CROSSREFS

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

Sequence in context: A167002 A227005 A054465 * A303630 A257547 A160703

Adjacent sequences: A118710 A118711 A118712 * A118714 A118715 A118716

KEYWORD

easy,sign

AUTHOR

Jonathan Vos Post, May 20 2006

EXTENSIONS

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

STATUS

approved