cp's OEIS Frontend

A071768 Determinant of the n X n matrix whose element (i,j) equals |i-j| (Mod 3).

%I A071768 #20 Jun 13 2015 00:50:33
%S A071768 0,-1,4,9,-10,4,18,-19,4,27,-28,4,36,-37,4,45,-46,4,54,-55,4,63,-64,4,
%T A071768 72,-73,4,81,-82,4,90,-91,4,99,-100,4,108,-109,4,117,-118,4,126,-127,
%U A071768 4,135,-136,4,144,-145,4,153,-154,4,162,-163,4,171,-172,4,180,-181,4,189
%N A071768 Determinant of the n X n matrix whose element (i,j) equals |i-j| (Mod 3).
%C A071768 (Mod 2) for n > 2 produces nothing but zeros.
%H A071768 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,1,1,1).
%F A071768 a(3k) = 4, a(3k+1) = 9*k, a(3k+2) = -9*k-1.
%F A071768 a(n) = -a(n-1)-a(n-2)+a(n-3)+a(n-4)+a(n-5). - _Colin Barker_, Sep 29 2014
%F A071768 G.f.: -x^2*(2*x+1)*(2*x^2+5*x-1) / ((x-1)*(x^2+x+1)^2). - _Colin Barker_, Sep 29 2014
%t A071768 Table[ Det[ Table[ Mod[ Abs[i - j], 3], {i, 1, n}, {j, 1, n}]], {n, 1, 65}]
%o A071768 (PARI) a(n) = matdet(matrix (n, n, i, j, abs(i-j) % 3)); \\ _Michel Marcus_, Sep 29 2014
%o A071768 (PARI) concat(0, Vec(-x^2*(2*x+1)*(2*x^2+5*x-1)/((x-1)*(x^2+x+1)^2) + O(x^100))) \\ _Colin Barker_, Sep 30 2014
%Y A071768 Cf. A071769 (with Mod 4).
%K A071768 sign,easy
%O A071768 1,3
%A A071768 _Robert G. Wilson v_, Jun 04 2002