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A118704
a(n) = determinant of n X n circulant matrix whose first row is the first n distinct Fibonacci numbers A000045(2), A000045(3), ... A000045(n+1).
1
1, -3, 18, -429, 24149, -3813376, 1513739413, -1575456727131, 4215561680804992, -29321025953223722025, 529210578655758192641625, -24875949855198086445567836160, 3047957640551011125902187378426905, -974921913036976554924444728974464589255
OFFSET
1,2
COMMENTS
a(n) alternates in sign.
LINKS
Eric Weisstein's World of Mathematics, Circulant Matrix.
EXAMPLE
a(2) = -3 because of the determinant -3 =
| 1, 2 |
| 2, 1 |.
a(5) = 24149 = determinant
| 1, 2, 3, 5, 8 |
| 8, 1, 2, 3, 5 |
| 5, 8, 1, 2, 3 |
| 3, 5, 8, 1, 2 |
| 2, 3, 5, 8, 1 |.
MAPLE
a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->
(<<0|1>, <1|1>>^(2+irem(n-i+j, n)))[1, 2])):
seq(a(n), n=1..15); # Alois P. Heinz, Oct 23 2009
CROSSREFS
See also: A048954 Wendt determinant of n-th circulant matrix C(n). A052182 Circulant of natural numbers. A066933 Circulant of prime numbers. A086459 Circulant of powers of 2.
Sequence in context: A370368 A303074 A181040 * A132514 A188801 A304780
KEYWORD
easy,sign
AUTHOR
Jonathan Vos Post, May 20 2006
EXTENSIONS
Corrected and extended by Alois P. Heinz, Oct 23 2009
STATUS
approved