A078924 Array of coefficients of characteristic polynomials of M_n, the n X n matrix with entries m_(i,j) = i mod j.

1, -1, 0, 1, 0, 0, -1, 0, 2, 0, 1, 0, -5, -2, 0, -1, 0, 17, 47, 34, 0, 1, 0, -30, -105, -72, 36, 0, -1, 0, 63, 426, 1143, 1272, 468, 0, 1, 0, -103, -936, -3668, -7412, -8424, -3744, 0, -1, 0, 169, 2104, 11859, 35084, 55856, 52680, 33696, 0, 1, 0, -250, -3883, -28047, -109953, -228920

Offset

0,9

Links

Table of n, a(n) for n=0..61.

Example

The characteristic polynomials of M_0, M_1, ..., M_4 are 1, -x + 0, x^2 + 0x + 0, -x^3 + 0x^2 + 2x + 0 and x^4 +0 x^3 - 5x^2 - 2x + 0, so the first 15 terms are 1; -1,0; 1,0,0; -1,0,2,0; 1,0,-5,-2,0.

Mathematica

c[0]={1}; c[n_] := Reverse[CoefficientList[CharacteristicPolynomial[Table[Mod[i, j], {i, 1, n}, {j, 1, n}], x], x]]; Flatten[c/@Range[0, 10]]

Crossrefs

Sequence in context: A128890 A196777 A318361 * A229141 A137526 A137525

Adjacent sequences: A078921 A078922 A078923 * A078925 A078926 A078927

Keyword

sign,tabl,easy

Author

Benoit Cloitre, Dec 15 2002

Status

approved