%I A086459
%S A086459 1,3,49,3375,923521,992436543,4195872914689,70110209207109375,
%T A086459 4649081944211090042881,1227102111503512992112190463,
%U A086459 1291749870339606615892191271170049,5429914198235566686555216227881787109375
%V A086459 1,-3,49,-3375,923521,-992436543,4195872914689,-70110209207109375,
%W A086459 4649081944211090042881,-1227102111503512992112190463,
%X A086459 1291749870339606615892191271170049,-5429914198235566686555216227881787109375
%N A086459 Determinant of the circulant matrix whose rows are formed by successively 
               rotating the vector (1,2,4,8,..2^(n-1)) right.
%C A086459 Note that if the rows are rotated left instead of right, the sign of 
               the terms for which n = 0 or 3 (mod 4) is reversed. The n eigenvalues 
               of these circulant matrices lie on the circle of radius 2(2^n - 1)/
               3 centered at x=(2^n - 1)/3, y=0. This sequence can be generalized 
               to bases other than 2 and similar results are true.
%D A086459 Richard Bellman, Introduction to Matrix Analysis, Second Edition, SIAM, 
               1970, pp. 242-3.
%D A086459 Philip J. Davis, Circulant Matrices, Second Edition, Chelsea, 1994.
%H A086459 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CirculantMatrix.html">Circulant Matrix</a>
%F A086459 a(n) = (-2^n+1)^(n-1)
%e A086459 a(3) = determinant of the matrix ((1,2,4),(4,1,2),(2,4,1)) = 49. [Corrected 
               by T. D. Noe (noe(AT)sspectra.com), Jan 22 2008]
%p A086459 restart:with (combinat):a:=n->mul(-stirling2(n,2), j=3..n): seq(a(n), 
               n=2..19);[From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 
               01 2009]
%t A086459 Table[x=2^Range[0, n-1]; m=Table[RotateRight[x, i-1], {i, n}]; Det[m], 
               {n, 12}]
%Y A086459 Cf. A048954 (circulant of binomial coefficients), A052182 (circulant 
               of natural numbers), A066933 (circulant of prime numbers).
%Y A086459 Sequence in context: A012223 A012100 A106842 this_sequence A063893 A145572 
               A034201
%Y A086459 Adjacent sequences: A086456 A086457 A086458 this_sequence A086460 A086461 
               A086462
%K A086459 easy,sign
%O A086459 1,2
%A A086459 T. D. Noe (noe(AT)sspectra.com), Jul 21 2003