|
|
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.
|
|
0
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|