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A158335 A triangle of matrix polynomials: m(n)=antisymmeticmatix(n).Transpose[antisymmeticmatix(n)]. 0

%I

%S 1,0,-1,1,-2,1,0,-9,6,-1,1,-12,38,-12,1,0,-25,100,-110,20,-1,1,-30,

%T 255,-452,255,-30,1,0,-49,490,-1519,1484,-511,42,-1,1,-56,924,-3976,

%U 6470,-3976,924,-56,1,0,-81,1512,-9324,21816,-21942,9240,-1548,72,-1,1,-90

%N A triangle of matrix polynomials: m(n)=antisymmeticmatix(n).Transpose[antisymmeticmatix(n)].

%C Row sums are:

%C {1, -1, 0, -4, 16, -16, 0, -64, 256, -256, 0,...}. Unsigned row sums are:

%C {1, 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144,...}.

%C Example matrix is:

%C M(3)={{2, -1, -1},

%C {-1, 2, -1},

%C {-1, -1, 2}}

%F m(n)=antisymmeticmatix(n).Transpose[antisymmeticmatix(n)];

%F out_(n,m)=coefficients(characteristicpolynomial(m(n),x),x).

%e {1},

%e {0, -1},

%e {1, -2, 1},

%e {0, -9, 6, -1},

%e {1, -12, 38, -12, 1},

%e {0, -25, 100, -110, 20, -1},

%e {1, -30, 255, -452, 255, -30, 1},

%e {0, -49, 490, -1519, 1484, -511, 42, -1},

%e {1, -56, 924, -3976, 6470, -3976, 924, -56, 1},

%e {0, -81, 1512, -9324, 21816, -21942, 9240, -1548, 72, -1},

%e {1, -90, 2445, -19320, 63090, -92252, 63090, -19320, 2445, -90, 1}

%t Clear[M, T, d, a, x, a0];

%t T[n_, m_, d_] := If[ m < n, (-1)^(n + m), If[m > n, -(-1)^(n + m), 0]];

%t M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}].Transpose[Table[T[n, m, d], {n, 1, d}, {m, 1, d}]];

%t Table[Det[M[d]], {d, 1, 10}];

%t Table[M[d], {d, 1, 10}]

%t Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];

%t a = Join[{{1}}, Table[CoefficientList[Expand[CharacteristicPolynomial[M[ n], x]], x], {n, 1, 10}]];

%t Flatten[a]; Join[{1}, Table[Apply[Plus, CoefficientList[Expand[ CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}]];

%Y A119467

%K sign,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 16 2009

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Last modified October 21 19:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)