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Search: id:A124034
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| A124034 |
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Tri-antidiagonal matrices of cental ones with upper negative one to give a triangular sequence: first element is negative one. k=1;m(n,m,d)=If[n + m - 1 == d && n > 1, k, If[n + m ==d, -1, If[n + m - 2 == d, -1, If[n == 1 && m == d, -k, 0]]]]. |
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+0
1
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| -1, -1, -1, 2, 2, 1, 1, 1, 1, -1, 1, 0, -1, 2, 1, 2, 0, 0, 4, 1, -1, -1, 0, -1, -6, -4, 2, 1, 1, 1, -1, -7, -3, 7, 1, -1, -2, -2, -1, 8, 6, -12, -7, 2, 1, -1, -1, -2, 10, 3, -23, -6, 10, 1, -1, -1, 0, 2, -12, -7, 34, 22, -18, -10, 2, 1, -2, 0, 0, -16, -4, 52, 16, -48, -9, 13, 1, -1, 1, 0, 2, 20, 13, -70, -46, 78, 47, -24, -13, 2, 1, -1, -1, 2, 22, 9
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Matrices: 1 X 1 {{-1}}, 2 X 2 {{-1, -1}, {1, -1}}, 3 X 3 {{0, -1, -1}, {-1, 1, -1}, {1, -1, 0}}, 4 X 4 {{0, 0, -1, -1}, {0, -1, 1, -1}, {-1, 1, -1, 0}, {1, -1, 0, 0}}, 5 X 5 {{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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k=1; m(n,m,d)=If[n + m - 1 == d && n > 1, k, If[n + m ==d, -1, If[n + m - 2 == d, -1, If[n == 1 && m == d, -k, 0]]]]
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EXAMPLE
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Triangular sequence:
{-1},
{-1, -1},
{2, 2, 1},
{1, 1, 1, -1},
{1, 0, -1, 2, 1},
{2, 0, 0, 4,1, -1},
{-1, 0, -1, -6, -4, 2, 1},
{1, 1, -1, -7, -3, 7, 1, -1},
{-2, -2, -1, 8, 6, -12, -7, 2, 1},
{-1, -1, -2, 10, 3, -23, -6, 10, 1, -1},
{-1, 0, 2, -12, -7, 34, 22, -18, -10, 2, 1}
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MATHEMATICA
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k = 1; An[d_] := Table[If[n + m - 1 == d && n > 1, k, If[n + m == d, -1, If[n + m - 2 == d, -1, If[n == 1 &&m == d, -k, 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: A054534 A085769 A102552 this_sequence A085978 A141044 A064284
Adjacent sequences: A124031 A124032 A124033 this_sequence A124035 A124036 A124037
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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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