A366551 Number of distinct characteristic polynomials for 3 X 3 matrices with entries from {0, 1, ..., n}.

1, 32, 513, 4407, 21393, 86620, 242057, 673623, 1467642, 3107487, 5836467, 11108595

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Robert P. P. McKone, The distinct characteristic polynomials for a(0)-a(6).

Formula

a(n) <= A366158(n) * A227776(n) * A016777(n).

Mathematica

mat[n_Integer?Positive] := mat[n] = Array[m, {n, n}]; flatMat[n_Integer?Positive] := flatMat[n] = Flatten[mat[n]]; charPolyMat[n_Integer?Positive] := charPolyMat[n] = FullSimplify[CoefficientList[Expand[CharacteristicPolynomial[mat[n], x]], x]]; a[d_Integer?Positive, 0] = 1; a[d_Integer?Positive, n_Integer?Positive] := a[d, n] = Length[DeleteDuplicates[Flatten[Table[Evaluate[charPolyMat[d]], ##] & @@ Table[{flatMat[d][[i]], 0, n}, {i, 1, d^2}], d^2 - 1]]]; Table[a[3, n], {n, 0, 7}]

Crossrefs

Cf. A366448 (2 X 2 matrices).

Cf. A366158 (determinants), A227776 (2nd order coefficients), A016777 (traces).

Cf. A272659.

Sequence in context: A035477 A109384 A248070 * A146124 A125489 A084486

Adjacent sequences: A366548 A366549 A366550 * A366552 A366553 A366554

Keyword

nonn,more

Author

Robert P. P. McKone, Oct 13 2023

Status

approved