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Search: id:A124021
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| A124021 |
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All ones and negatives ones tri-antidiagonal matrices like as characteristic polynomial triangular sequence: M(3)={{0, -1, 1}, {-1, 1, -1}, {1, -1, 0}}. |
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+0
1
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| 1, 1, -1, 0, 2, 1, 1, 3, 1, -1, -1, -4, -3, 2, 1, 0, -4, -2, 6, 1, -1, -1, 4, 3, -10, -6, 2, 1, -1, 5, 1, -17, -5, 9, 1, -1, 0, -6, -3, 24, 16, -16, -9, 2, 1, -1, -7, -2, 34, 11, -39, -8, 12, 1, -1, 1, 8, 6, -44, -29, 62, 38, -22, -12, 2, 1, 0, 8, 4, -60, -18, 114, 30, -70, -11, 15, 1, -1, 1, -8, -6, 76, 49, -166, -106, 118, 69, -28, -15, 2, 1, 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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Determinants of matrices: Table[Det[An[d]], {d, 1, 20}] {1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0} Matrices: {{1}}, {{-1, 1}, {1, -1}}, {{0, -1, 1}, {-1, 1, -1}, {1, -1, 0}}, {{0, 0, -1, 1}, {0, -1, 1, -1}, {-1, 1, -1, 0}, {1, -1, 0, 0}}, {{0, 0, 0, -1, 1}, {0, 0, -1, 1, -1}, {0, -1, 1, -1, 0}, {-1, 1, -1, 0, 0}, {1, -1, 0, 0,0}}
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FORMULA
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M(d)=If[n + m - 1 == d, 1, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]]
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EXAMPLE
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Triangular sequence:
{1},
{1, -1},
{0, 2, 1},
{1, 3, 1, -1},
{-1, -4, -3, 2, 1},
{0, -4, -2, 6, 1, -1},
{-1, 4,3, -10, -6, 2, 1},
{-1, 5, 1, -17, -5, 9, 1, -1}
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MATHEMATICA
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An[d_] := Table[If[n + m - 1 == d, 1, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]], {n, 1, d}, {m, 1, d}]; Join[An[1], Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]
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CROSSREFS
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Sequence in context: A167269 A105535 A108888 this_sequence A109626 A160182 A098824
Adjacent sequences: A124018 A124019 A124020 this_sequence A124022 A124023 A124024
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KEYWORD
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sign,tabl,uned,probation
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Oct 31 2006
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