A123735 - OEIS

%I #3 Oct 12 2012 14:55:30

%S 0,0,-1,-1,0,1,-2,3,0,-1,0,4,-5,0,1,2,-3,-6,7,0,-1,3,-12,10,8,-9,0,1,

%T 0,-9,30,-21,-10,11,0,-1,-3,12,11,-56,36,12,-13,0,1,-4,30,-60,-1,90,

%U -55,-14,15,0,-1,0,16,-100,168,-29,-132,78,16,-17,0,1

%N zero centered pentadiagonal matrices as a triangular sequence of Characteristic polynomials: Matrix model: M4={{0, -1, -1, 0}, {-1, 0, -1, -1}, {-1, -1, 0, -1}, {0, -1, -1, 0}}.

%C Pentadiagonals give cycles in the graphs. Absolute value of the Row sum is new as well: Table[Sum[Abs[a[[n]][[m]]], {m, 1, n}], {n, 1, Length[a]}] {0, 1, 2, 6, 10, 19, 43, 82, 144, 270, 557}

%F m(n,m,d)=If[ n == m, 0, If[n == m - 1 || n ==m + 1, -1, If[n == m - 2 || n == m + 2, -1, 0]]]

%e Triangular sequence:

%e {0},

%e {0, -1},

%e {-1, 0, 1},

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

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

%e {2, -3, -6, 7, 0, -1},

%e {3, -12, 10, 8, -9, 0, 1},

%e {0, -9, 30, -21, -10, 11, 0, -1},

%e {-3, 12, 11, -56, 36, 12, -13, 0, 1},

%e {-4, 30, -60, -1, 90, -55, -14, 15, 0, -1},

%e {0, 16, -100, 168, -29, -132, 78, 16, -17, 0, 1}

%t T[n_, m_, d_] := If[ n == m, 0, If[n == m - 1 || n == m + 1, -1, If[n == m - 2 || n == m + 2, -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

%O 1,7

%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 14 2006