|
%I #6 Aug 09 2015 01:43:19
%S 1,0,-1,-1,0,1,-9,3,3,-1,96,32,-20,-4,1,1250,-125,-250,25,10,-1,
%T -19440,-5184,2592,576,-93,-12,1,-352947,16807,50421,-2401,-2058,98,
%U 21,-1,7340032,1572864,-753664,-147456,24064,3840,-272,-24,1,172186884,-4782969,-19131876,531441,708588,-19683,-9720,270,36
%N A triangular sequence from the Z/nZ matrix addition tables as in sequence A095897 as coefficients of characteristic polynomials: M(n,m)=Mod[n + m, d] for n <=m<=d.
%C Row sums are:
%C {1, -1, 0, -4, 105, 909, -21560, -290060, 8039385, 149482970, -4868582664};
%C These are _Gary W. Adamson_'s matrices: I plugged them into my existing matrix program.
%F M(n,m)=Mod[n + m, d] for n <=m<=d; p(x,n)=CharacteristicPolynomial(M(n,m)); out_n,m=Coefficients(p(x,n));
%e {1},
%e {0, -1},
%e {-1,0, 1},
%e {-9, 3, 3, -1},
%e {96, 32, -20, -4, 1},
%e {1250, -125, -250, 25, 10, -1},
%e {-19440, -5184, 2592, 576, -93, -12, 1},
%e {-352947, 16807, 50421, -2401, -2058, 98, 21, -1},
%e {7340032, 1572864, -753664, -147456, 24064, 3840, -272, -24, 1},
%e {172186884, -4782969, -19131876, 531441, 708588, -19683, -9720, 270, 36, -1},
%e {-4500000000, -800000000, 380000000, 64000000, -11050000, -1680000, 132000, 16000, -625, -40, 1}
%t M[d_] := Table[Mod[n + m, d], {n, 0, d - 1}, {m, 0, d - 1}]; a1 = Table[M[d], {d, 1, 10}]; Table[Det[M[d]], {d, 1, 10}]; g = Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{1}}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a] MatrixForm[a];
%Y Cf. A095897.
%K uned,tabl,sign
%O 1,7
%A _Roger L. Bagula_ and _Gary W. Adamson_, May 02 2008
|
