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Search: id:A124028
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| A124028 |
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Center anitdiagonal four in a tri-antidiagonal n-th Matrix generated triangular sequence: first element as 4==m[1,1,1]. |
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1
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| 4, 4, -1, -15, 2, 1, -56, 18, 4, -1, 209, -34, -33, 2, 1, 780, -259, -128, 36, 4, -1, -2911, 484, 738, -70, -51, 2, 1, -10864, 3620, 2824, -842, -200, 54, 4, -1, 40545, -6756, -14178, 1614, 1591, -106, -69, 2, 1, 151316, -50437, -53888, 16564, 6164, -1749, -272, 72, 4, -1, -564719, 94118, 251811, -31514, -39629
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These mastrices and triangular sequences are machine generated: all we have done is invent the matrix form "tri-antidiagonal matrices" and get a way to compute it. Matrices: {{4}}, {{-1, 4}, {4, -1}}, {{0, -1, 4}, {-1, 4, -1}, {4, -1, 0}}, {{0, 0, -1, 4}, {0, -1, 4, -1}, {-1, 4, -1, 0}, {4, -1, 0, 0}}, {{0, 0, 0, -1, 4}, {0, 0, -1, 4, -1}, {0, -1, 4, -1, 0}, {-1, 4, -1, 0, 0}, {4, -1, 0, 0,0}}
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FORMULA
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m(n,m,d)=If[n + m - 1 == d, 4, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]]
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EXAMPLE
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Triangular sequence:
{4},
{4, -1},
{-15, 2, 1},
{-56, 18, 4, -1},
{209, -34, -33, 2, 1},
{780, -259, -128, 36, 4, -1},
{-2911, 484, 738, -70, -51, 2, 1},
{-10864, 3620, 2824, -842, -200, 54, 4, -1},
{40545, -6756, -14178, 1614, 1591, -106, -69, 2, 1}
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MATHEMATICA
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An[d_] := Table[If[n + m - 1 == d, 4, 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: A140313 A102323 A145902 this_sequence A123966 A079507 A098364
Adjacent sequences: A124025 A124026 A124027 this_sequence A124029 A124030 A124031
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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), Nov 01 2006
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