A123735 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}}.

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, 0, -9, 30, -21, -10, 11, 0, -1, -3, 12, 11, -56, 36, 12, -13, 0, 1, -4, 30, -60, -1, 90, -55, -14, 15, 0, -1, 0, 16, -100, 168, -29, -132, 78, 16, -17, 0, 1

Offset

1,7

Comments

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}

Links

Table of n, a(n) for n=1..66.

Formula

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]]]

Example

Triangular sequence:
{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},
{0, -9, 30, -21, -10, 11, 0, -1},
{-3, 12, 11, -56, 36, 12, -13, 0, 1},
{-4, 30, -60, -1, 90, -55, -14, 15, 0, -1},
{0, 16, -100, 168, -29, -132, 78, 16, -17, 0, 1}

Mathematica

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]

Crossrefs

Sequence in context: A357720 A357712 A298159 * A155839 A229615 A359177

Adjacent sequences: A123732 A123733 A123734 * A123736 A123737 A123738

Keyword

uned,sign

Author

Roger L. Bagula and Gary W. Adamson, Nov 14 2006

Status

approved