A138064 A triangular sequence from the Z/nZ matrix addition tables as in sequence A095897 as coefficients of characteristic polynomials: M(n,m)=Mod[n + m, d] for n <=m<=d.

1, 0, -1, -1, 0, 1, -9, 3, 3, -1, 96, 32, -20, -4, 1, 1250, -125, -250, 25, 10, -1, -19440, -5184, 2592, 576, -93, -12, 1, -352947, 16807, 50421, -2401, -2058, 98, 21, -1, 7340032, 1572864, -753664, -147456, 24064, 3840, -272, -24, 1, 172186884, -4782969, -19131876, 531441, 708588, -19683, -9720, 270, 36

Offset

1,7

Comments

Row sums are:

{1, -1, 0, -4, 105, 909, -21560, -290060, 8039385, 149482970, -4868582664};

These are Gary W. Adamson's matrices: I plugged them into my existing matrix program.

Links

Table of n, a(n) for n=1..54.

Formula

M(n,m)=Mod[n + m, d] for n <=m<=d; p(x,n)=CharacteristicPolynomial(M(n,m)); out_n,m=Coefficients(p(x,n));

Example

{1},
{0, -1},
{-1,0, 1},
{-9, 3, 3, -1},
{96, 32, -20, -4, 1},
{1250, -125, -250, 25, 10, -1},
{-19440, -5184, 2592, 576, -93, -12, 1},
{-352947, 16807, 50421, -2401, -2058, 98, 21, -1},
{7340032, 1572864, -753664, -147456, 24064, 3840, -272, -24, 1},
{172186884, -4782969, -19131876, 531441, 708588, -19683, -9720, 270, 36, -1},
{-4500000000, -800000000, 380000000, 64000000, -11050000, -1680000, 132000, 16000, -625, -40, 1}

Mathematica

M[d_] := Table[Mod[n + m, d], {n, 0, d - 1}, {m, 0, d - 1}]; a1 = Table[M[d], {d, 1, 10}]; Table[Det[M[d]], {d, 1, 10}]; g = Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{1}}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a] MatrixForm[a];

Crossrefs

Cf. A095897.

Sequence in context: A021842 A363848 A011112 * A063569 A037921 A327135

Adjacent sequences: A138061 A138062 A138063 * A138065 A138066 A138067

Keyword

uned,tabl,sign

Author

Roger L. Bagula and Gary W. Adamson, May 02 2008

Status

approved