%I A138064
%S A138064 1,0,1,1,0,1,9,3,3,1,96,32,20,4,1,1250,125,250,25,10,1,19440,5184,2592,
               576,
%T A138064 93,12,1,352947,16807,50421,2401,2058,98,21,1,7340032,1572864,753664,147456,
%U A138064 24064,3840,272,24,1,172186884,4782969,19131876,531441,708588,19683,9720,
               270,36
%V A138064 1,0,-1,-1,0,1,-9,3,3,-1,96,32,-20,-4,1,1250,-125,-250,25,10,-1,-19440,
               -5184,2592,576,
%W A138064 -93,-12,1,-352947,16807,50421,-2401,-2058,98,21,-1,7340032,1572864,-753664,
               -147456,
%X A138064 24064,3840,-272,-24,1,172186884,-4782969,-19131876,531441,708588,-19683,
               -9720,270,36
%N A138064 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 A138064 Row sums are:
%C A138064 {1, -1, 0, -4, 105, 909, -21560, -290060, 8039385, 149482970, -4868582664};
%C A138064 These are Gary Adamson's matrices: I plugged them into my existing matrix 
               program.
%F A138064 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 A138064 {1},
%e A138064 {0, -1},
%e A138064 {-1,0, 1},
%e A138064 {-9, 3, 3, -1},
%e A138064 {96, 32, -20, -4, 1},
%e A138064 {1250, -125, -250, 25, 10, -1},
%e A138064 {-19440, -5184, 2592, 576, -93, -12, 1},
%e A138064 {-352947, 16807, 50421, -2401, -2058, 98, 21, -1},
%e A138064 {7340032, 1572864, -753664, -147456, 24064, 3840, -272, -24, 1},
%e A138064 {172186884, -4782969, -19131876, 531441, 708588, -19683, -9720, 270, 
               36, -1},
%e A138064 {-4500000000, -800000000, 380000000, 64000000, -11050000, -1680000, 132000, 
               16000, -625, -40, 1}
%t A138064 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 A138064 Cf. A095897.
%Y A138064 Sequence in context: A019721 A021842 A011112 this_sequence A063569 A037921 
               A019878
%Y A138064 Adjacent sequences: A138061 A138062 A138063 this_sequence A138065 A138066 
               A138067
%K A138064 uned,tabl,sign
%O A138064 1,7
%A A138064 Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), May 02 
               2008