A124035 - OEIS

%I #10 Aug 26 2016 20:31:06

%S -1,-1,-1,-2,0,1,-1,3,1,-1,1,4,-3,-2,1,2,0,-8,2,3,-1,1,-6,-5,12,0,-4,

%T 1,-1,-7,9,15,-15,-3,5,-1,-2,0,21,-6,-30,16,7,-6,1,-1,9,12,-42,-9,49,

%U -14,-12,7,-1,1,10,-18,-48,63,42,-70,8,18,-8,1

%N Tridiagonal matrices of central ones with lower negative one to give a triangular sequence: first element is negative one. m(n,m,d)=If[ n == m && n < d && m < d, 1, If[n == m - 1 || n == m + 1, -1, If[n == m == d, -1, 0]].

%C The 4 X 4 is a g(u,v) type of matrix where Minkowski is n(u,v)={1,1,1,-1}: single hyperbolic index. Matrices: 1 X 1 {{-1}} 2 X 2 {{1, -1}, {-1, -1}} 3 X 3 {{1, -1, 0}, {-1, 1, -1}, {0, -1, -1}} 4 X 4 {{1, -1, 0, 0}, {-1, 1, -1, 0}, {0, -1, 1, -1}, {0, 0, -1, -1}} 5 X 5 {{1, -1, 0, 0, 0}, {-1, 1, -1, 0, 0}, {0, -1, 1, -1, 0}, {0, 0, -1, 1, -1}, {0, 0, 0, -1, -1}

%F m(n,m,d)=If[ n == m && n < d && m < d, 1, If[n == m - 1 || n == m + 1, -1, If[n == m == d, -1, 0]]

%e Triangular sequence:

%e {{-1}},

%e {-1, -1},

%e {-2, 0, 1},

%e {-1, 3, 1, -1},

%e {1, 4, -3, -2,1},

%e {2, 0, -8, 2, 3, -1},

%e {1, -6, -5, 12, 0, -4, 1},

%e {-1, -7, 9, 15, -15, -3, 5, -1},

%e {-2, 0, 21, -6, -30, 16, 7, -6, 1},

%t T[n_, m_, d_] := If[ n == m && n < d && m < d, 1, If[n == m - 1 || n == m + 1, -1, If[n == m == d, -1, 0]]] M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}] Table[M[d], {d, 1, 10}] Table[Det[M[d]], {d, 1, 10}] Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}] a = Join[{M[1]}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], { d, 1, 10}]] Flatten[a] MatrixForm[a]

%K uned,sign,tabl

%O 1,4

%A _Roger L. Bagula_, Nov 02 2006