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A118713
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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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8
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4, -20, 361, -3567, 218053, -3455872, 736439027, -16245418225, 1519211613654, -37662452460912, 20199655476042865, -643524421698841536, 46513669467992431114, -3754367220494585505280, 277686193779526116536293, -123973821931125256333959105, 20103033234038999233385180658
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..17.
Eric Weisstein's World of Mathematics, Circulant Matrix.
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EXAMPLE
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a(2) = -20 = determinant
|4,6|
|6,4|.
a(3) = 361 = 19^2 = determinant
|4,6,9|
|9,4,6|
|6,9,4|.
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MAPLE
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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) ;
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A001358, A048954, A052182, A066933, A086459, A086569.
Sequence in context: A167002 A227005 A054465 * A303630 A257547 A160703
Adjacent sequences: A118710 A118711 A118712 * A118714 A118715 A118716
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KEYWORD
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easy,sign
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AUTHOR
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Jonathan Vos Post, May 20 2006
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EXTENSIONS
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Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Aug 23 2007
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STATUS
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approved
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