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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Semiprime analogue 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
| Eric Weisstein's World of Mathematics, Circulant Matrix.
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EXAMPLE
| 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
| 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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CROSSREFS
| Cf. A001358, A048954, A052182, A066933, A086459, A086569.
Sequence in context: A012797 A167002 A054465 * A160703 A132511 A144989
Adjacent sequences: A118710 A118711 A118712 * A118714 A118715 A118716
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KEYWORD
| easy,sign
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 20 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Aug 23 2007
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