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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.
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%I #20 Feb 16 2023 05:12:19

%S 4,-20,361,-3567,218053,-3455872,736439027,-16245418225,1519211613654,

%T -37662452460912,20199655476042865,-643524421698841536,

%U 46513669467992431114,-3754367220494585505280,277686193779526116536293,-123973821931125256333959105,20103033234038999233385180658

%N 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.

%C 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.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.

%e a(2) = -20 = determinant

%e |4,6|

%e |6,4|.

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

%e |4,6,9|

%e |9,4,6|

%e |6,9,4|.

%p A118713 := proc(n)

%p local C,r,c ;

%p C := Matrix(1..n,1..n) ;

%p for r from 1 to n do

%p for c from 1 to n do

%p C[r,c] := A001358(1+((c-r) mod n)) ;

%p end do:

%p end do:

%p LinearAlgebra[Determinant](C) ;

%p end proc:

%p seq(A118713(n),n=1..13) ;

%t nmax = 13;

%t sp = Select[Range[3 nmax], PrimeOmega[#] == 2&];

%t a[n_] := Module[{M}, M[1] = sp[[1 ;; n]];

%t M[k_] := M[k] = RotateRight[M[k - 1]];

%t Det[Table[M[k], {k, 1, n}]]];

%t Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, Feb 16 2023 *)

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

%K easy,sign

%O 1,1

%A _Jonathan Vos Post_, May 20 2006

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Aug 23 2007