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Search: id:A136458
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| A136458 |
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Triangle of coefficients of the characteristic polynomial of an bi-orthogonnal nXn matrix: h(i,j)=If[i - j == 0, 1, If[Abs[i - j] - n/2 == 0, -1, 0]];i,j<=n; example n=4: {{1, 0, -1, 0}, {0, 1, 0, -1}, {-1, 0, 1, 0}, {0, -1, 0, 1}}. |
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+0
1
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| 1, 1, -1, 0, -2, 1, 1, -3, 3, -1, 0, 0, 4, -4, 1, 1, -5, 10, -10, 5, -1, 0, 0, 0, -8, 12, -6, 1, 1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 16, -32, 24, -8, 1, 1, -9, 36, -84, 126, -126, 84, -36, 9, -1, 0, 0, 0, 0, 0, -32, 80, -80, 40, -10, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1}
These matrices are related to binary digital signal processing.
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REFERENCES
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http://www.ee.cityu.edu.hk/~eekwwong/ee40214/chapter3.pdf
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FORMULA
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If[i - j == 0, 1, If[Abs[i - j] - n/2 == 0, -1, 0]],
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EXAMPLE
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{1},
{1, -1},
{0, -2, 1},
{1, -3, 3, -1},
{0, 0, 4, -4, 1},
{1, -5, 10, -10, 5, -1},
{0, 0, 0, -8, 12, -6, 1},
{1, -7, 21, -35, 35, -21, 7, -1},
{0, 0, 0, 0, 16, -32, 24, -8, 1},
{1, -9, 36, -84, 126, -126, 84, -36, 9, -1},
{0, 0, 0, 0, 0, -32, 80, -80, 40, -10, 1}
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MATHEMATICA
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Clear[B] B[n_] := Table[Table[If[i -j == 0, 1, If[Abs[i - j] - n/2 == 0, -1, 0]], {i, 1, n}], {j, 1, n}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[B[n], x], x], {n, 1, 10}]]; Flatten[a] Join[{1}, Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[B[n], x], x]], {n, 1, 10}]];
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CROSSREFS
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Adjacent sequences: A136455 A136456 A136457 this_sequence A136459 A136460 A136461
Sequence in context: A078802 A108482 A124750 this_sequence A048805 A129571 A034931
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
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