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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. 8
 4, -20, 361, -3567, 218053, -3455872, 736439027, -16245418225, 1519211613654, -37662452460912, 20199655476042865, -643524421698841536, 46513669467992431114, -3754367220494585505280, 277686193779526116536293, -123973821931125256333959105, 20103033234038999233385180658 (list; graph; refs; listen; history; text; internal format)
 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 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: 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

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Last modified March 25 16:18 EDT 2023. Contains 361528 sequences. (Running on oeis4.)