A138088 Triangle read by rows: coefficients of characteristic polynomials of the Z/nZ addition matrices using PolynomialMod[p(x,n),n] in Mathematica. ( Polynomials/nZ): P(x, n) = If[Mod[n, 4] == 0, x^n, If[Mod[n, 2] == 1, If[n == 0, 1, (n - 1)*x^n], (n/2)x^(n - 2) + x^n]].

1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 1

Offset

1,9

Comments

Row sums are: {1, 0, 2, 2, 1, 4, 4, 6, 1, 8, 6, ...};

Links

Table of n, a(n) for n=1..65.

Formula

P(x, n) = If[Mod[n, 4] == 0, x^n, If[Mod[n, 2] == 1, If[n == 0, 1, (n - 1)*x^n], (n/2)x^(n - 2) + x^n]]; out_n,m=Coefficients(P(x,n)).

Example

{1},
{0}, : Mathematica leaves out this zero in Flatten[];
{1, 0, 1},
{0, 0, 0, 2},
{0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 4},
{0, 0, 0, 0, 3, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 6},
{0, 0, 0, 0, 0, 0, 0, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 8},
{0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 1}

Mathematica

(* Polynomial form*) Clear[P, x]; P[x_, n_] :=P[x, n] = If[Mod[n, 4] ==0, x^n, If[Mod[n, 2] == 1, If[n == 0, 1, (n - 1)*x^n], (n/2)x^(n - 2) + x^n]]; g1 = Table[P[x, n], {n, 0, 10}] (* matrix form*) M[d_] := Table[Mod[n + m, d], {n, 0, d - 1}, {m, 0, d - 1}]; a = Join[{{1}}, Table[CoefficientList[PolynomialMod[Det[M[d] - x*IdentityMatrix[d]], d], x], {d, 1, 10}]]; Flatten[a]

Crossrefs

Sequence in context: A178408 A073345 A216511 * A112765 A105966 A318950

Adjacent sequences: A138085 A138086 A138087 * A138089 A138090 A138091

Keyword

nonn,uned,tabf

Author

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

Status

approved