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A118702 a(n) = determinant of n X n circulant matrix whose first row is the first n Lucas numbers A000032, from L(0) to L(n-1).

%I A118702 #10 Feb 16 2025 08:33:01
%S A118702 2,3,18,0,8347,-861952,391524998,-359089453125,893329160995712,
%T A118702 -5499366235206395112,87687141416511254851323,
%U A118702 -3590079701896396800000000000,381284797406693371431803926245802,-105147887074796935457211770823970013737
%N A118702 a(n) = determinant of n X n circulant matrix whose first row is the first n Lucas numbers A000032, from L(0) to L(n-1).
%H A118702 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.
%e A118702 a(4) = 0 because of the singular matrix:
%e A118702 [2, 1, 3, 4]
%e A118702 [4, 2, 1, 3]
%e A118702 [3, 4, 2, 1]
%e A118702 [1, 3, 4, 2].
%t A118702 circ[w_] := NestList[RotateRight, w, Length[w] - 1]; Table[ Det[ circ[ LucasL@ Range[0, n - 1]]], {n, 10}] (* _Giovanni Resta_, Jun 16 2016 *)
%Y A118702 A000032 Lucas numbers (beginning at 2): L(n) = L(n-1) + L(n-2). 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.
%Y A118702 Cf. A000032, A048954, A052182, A066933, A086459, A086569.
%K A118702 easy,sign
%O A118702 1,1
%A A118702 _Jonathan Vos Post_, May 20 2006
%E A118702 Corrected and extended by _Giovanni Resta_, Jun 16 2016