A078924 - OEIS

%I #15 Dec 04 2024 11:46:50

%S 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,

%T 36,0,-1,0,63,426,1143,1272,468,0,1,0,-103,-936,-3668,-7412,-8424,

%U -3744,0,-1,0,169,2104,11859,35084,55856,52680,33696,0,1,0,-250,-3883,-28047,-109953,-228920,-170972,240720,388800,0

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

%H Robert Israel, <a href="/A078924/b078924.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)

%e 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.

%p printf("[1]\n"):

%p for n from 1 to 10 do

%p   M:= Matrix(n,n,(i,j) -> i mod j);

%p   P:= (-1)^n*LinearAlgebra:-CharacteristicPolynomial(M,t);

%p   C:=  seq(coeff(P,t,i),i=n..0,-1);

%p   printf("%a\n",[C]);

%p od: # _Robert Israel_, Dec 04 2024

%t 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]]

%K sign,tabl,easy

%O 0,9

%A _Benoit Cloitre_, Dec 15 2002