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Search: id:A124035
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| A124035 |
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Tridiagonal matrices of cental ones with lower negative one to give a triangular sequence: first element is negative one. m(n,m,d)=If[ n == m && n < d && m < d, 1, If[n == m - 1 || n == m + 1, -1, If[n == m == d, -1, 0]]. |
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+0
1
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| -1, -1, -1, -2, 0, 1, -1, 3, 1, -1, 1, 4, -3, -2, 1, 2, 0, -8, 2, 3, -1, 1, -6, -5, 12, 0, -4, 1, -1, -7, 9, 15, -15, -3, 5, -1, -2, 0, 21, -6, -30, 16, 7, -6, 1, -1, 9, 12, -42, -9, 49, -14, -12, 7, -1, 1, 10, -18, -48, 63, 42, -70, 8, 18, -8, 1
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The 4 X 4 is a g(u,v) type of matrix where Minkowski is n(u,v)={1,1,1,-1}: single hyperbolic indice. Matrices: 1 X 1 {{-1}} 2 X 2 {{1, -1}, {-1, -1}} 3 X 3 {{1, -1, 0}, {-1, 1, -1}, {0, -1, -1}} 4 X 4 {{1, -1, 0, 0}, {-1, 1, -1, 0}, {0, -1, 1, -1}, {0, 0, -1, -1}} 5 X 5 {{1, -1, 0, 0, 0}, {-1, 1, -1, 0, 0}, {0, -1, 1, -1, 0}, {0, 0, -1, 1, -1}, {0, 0, 0, -1, -1}
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FORMULA
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m(n,m,d)=If[ n == m && n < d && m < d, 1, If[n == m - 1 || n == m + 1, -1, If[n == m == d, -1, 0]]
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EXAMPLE
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Triangular sequence:
{{-1}},
{-1, -1},
{-2, 0, 1},
{-1, 3, 1, -1},
{1, 4, -3, -2,1},
{2, 0, -8, 2, 3, -1},
{1, -6, -5, 12, 0, -4, 1},
{-1, -7, 9, 15, -15, -3, 5, -1},
{-2, 0, 21, -6, -30, 16, 7, -6, 1},
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MATHEMATICA
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T[n_, m_, d_] := If[ n == m && n < d && m < d, 1, If[n == m - 1 || n == m + 1, -1, If[n == m == d, -1, 0]]] M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}] Table[M[d], {d, 1, 10}] Table[Det[M[d]], {d, 1, 10}] Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}] a = Join[{M[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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Adjacent sequences: A124032 A124033 A124034 this_sequence A124036 A124037 A124038
Sequence in context: A079685 A079603 A055186 this_sequence A140129 A029347 A058725
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KEYWORD
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uned,probation,sign
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2006
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