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Search: id:A124018
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| A124018 |
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Triangular sequence from tri-antidigonal 2's center matices characteristic polynomials. |
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+0
2
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| 2, 2, -1, -3, 2, 1, -4, 6, 2, -1, 5, -10, -9, 2, 1, 6, -19, -16, 12, 2, -1, -7, 28, 42, -22, -15, 2, 1, -8, 44, 68, -74, -28, 18, 2, -1, 9, -60, -138, 126, 115, -34, -21, 2, 1, 10, -85, -208, 316, 202, -165, -40, 24, 2, -1, -11, 110, 363, -506, -605, 296, 224, -46, -27, 2, 1, -12, 146, 518, -1059, -1008, 1032, 408, -292, -52
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Matrices: {{2}}, {{-1, 2}, {2, -1}}, {{0, -1, 2}, {-1, 2, -1}, {2, -1, 0}}, {{0, 0, -1,2}, {0, -1, 2, -1}, {-1, 2, -1, 0}, {2, -1, 0, 0}}, {{0, 0, 0, -1, 2}, {0, 0, -1, 2, -1}, {0, -1, 2, -1, 0}, {-1, 2, -1, 0, 0}, {2, -1, 0, 0, 0}} The determinants count from two: Table[Det[An[d]], {d, 1, 20}] {2, -3, -4, 5, 6, -7, -8, 9, 10, -11, -12, 13, 14, -15, -16, 17,18, -19, -20, 21}
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FORMULA
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a(n,m,d) = If[n + m - 1 == d, 2, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]]
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EXAMPLE
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Triangular sequence:
{2},
{2, -1},
{-3,2, 1},
{-4, 6, 2, -1},
{5, -10, -9, 2, 1},
{6, -19, -16, 12, 2, -1},
{-7,28, 42, -22, -15, 2, 1},
{-8, 44, 68, -74, -28,18, 2, -1},
{9, -60, -138, 126, 115, -34, -21, 2, 1}
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MATHEMATICA
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An[d_] := Table[If[n + m - 1 == d, 2, 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: A053274 A026146 A094366 this_sequence A111709 A039996 A039994
Adjacent sequences: A124015 A124016 A124017 this_sequence A124019 A124020 A124021
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KEYWORD
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uned,probation,sign
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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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