A140059 Triangle read by rows: characteristic polynomials of Z/nZ addition tables considered as matrices.

1, 1, 0, 1, 0, -1, 1, -3, -3, 9, 1, -4, -20, 32, 96, 1, -10, -25, 250, 125, -1250, 1, -12, -93, 576, 2592, -5184, -19440, 1, -21, -98, 0, 2058, 2401, 50421, 16807, 352947, 1, -24, -272, 3840, 24064, -147456, -753664, 1572864, 7340032

Offset

0,8

Comments

The n-th row of the triangle is the characteristic polynomial of n-th order, Z/nZ addition table considered as a matrix.

The determinant of n-th order matrix (irrespective of sign) is the rightmost term of n-th order polynomial.

Links

Table of n, a(n) for n=0..45.

Example

Addition table Z/3Z = [0,1,2; 1,2,0; 2,0,1]. Considered as a matrix, the characteristic polynomial = x^3 - 3x^2 - 3x + 9.
First few characteristic polynomials are:
1;
x   + 0;
x^2 + 0x    - 1;
x^3 - 3x^2  - 3x    + 9;
x^4 - 4x^3  - 20x^2 + 32x      + 96;
x^5 - 10x^4 - 25x^3 + 250x^2   + 125x     - 1250;
x^6 - 12x^5 - 93x^4 + 576x^3   + 2592x^2  - 5194x     - 19440;
x^7 - 21x^6 - 98x^5 +   0x^4   + 2058x^3  - 50421x^2  - 16807x    + 352947;
x^8 - 24x^7 - 272x^6 + 3840x^5 + 24064x^4 - 147456x^3 - 753664x^2 + 1572864x + 7340032;

Crossrefs

Cf. A007070, A140044, A140045, A095897.

Sequence in context: A109695 A372038 A010610 * A324895 A070517 A290408

Adjacent sequences: A140056 A140057 A140058 * A140060 A140061 A140062

Keyword

sign,tabl

Author

Gary W. Adamson, May 03 2008

Extensions

Missing (zero) terms inserted by Michel Marcus, Apr 14 2013

Status

approved