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Search: id:A138064
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| A138064 |
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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. |
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+0
1
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| 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, -93, -12, 1, -352947, 16807, 50421, -2401, -2058, 98, 21, -1, 7340032, 1572864, -753664, -147456, 24064, 3840, -272, -24, 1, 172186884, -4782969, -19131876, 531441, 708588, -19683, -9720, 270, 36
(list; table; graph; listen)
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OFFSET
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1,7
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COMMENT
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Row sums are:
{1, -1, 0, -4, 105, 909, -21560, -290060, 8039385, 149482970, -4868582664};
These are Gary Adamson's matrices: I plugged them into my existing matrix program.
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FORMULA
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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));
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EXAMPLE
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{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, -93, -12, 1},
{-352947, 16807, 50421, -2401, -2058, 98, 21, -1},
{7340032, 1572864, -753664, -147456, 24064, 3840, -272, -24, 1},
{172186884, -4782969, -19131876, 531441, 708588, -19683, -9720, 270, 36, -1},
{-4500000000, -800000000, 380000000, 64000000, -11050000, -1680000, 132000, 16000, -625, -40, 1}
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MATHEMATICA
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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];
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CROSSREFS
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Cf. A095897.
Sequence in context: A019721 A021842 A011112 this_sequence A063569 A037921 A019878
Adjacent sequences: A138061 A138062 A138063 this_sequence A138065 A138066 A138067
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), May 02 2008
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