OFFSET
1,9
COMMENTS
Row sums are: {1, 0, 2, 2, 1, 4, 4, 6, 1, 8, 6, ...};
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
KEYWORD
nonn,uned,tabf
AUTHOR
Roger L. Bagula and Gary W. Adamson, May 02 2008
STATUS
approved