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Search: id:A124022
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| A124022 |
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Triangular sequence from the characteristic polynomials of the SL(n,Z)/ determiants {1,-1} type triantidiagonal 2 center with one upper, -1 side antidiagonal above and below: M(3)={{0, -1, 1}, {-1, 2, -1}, {2, -1, 0}}. |
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+0
1
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| 1, 1, -1, -1, 2, 1, -1, 4, 2, -1, 1, -6, -7, 2, 1, 1, -9, -12, 10, 2, -1, -1, 12, 26, -18, -13, 2, 1, -1, 16, 40, -52, -24, 16, 2, -1, 1, -20, -70, 86, 87, -30, -19, 2, 1, 1, -25, -100, 190, 150, -131, -36, 22, 2, -1, -1, 30, 155, -294, -403, 232, 184, -42, -25, 2, 1, -1, 36, 210, -553, -656, 736, 332, -246, -48, 28, 2, -1, 1, -42
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Matrices: {{1}}, {{-1, 1}, {2, -1}}, {{0, -1, 1}, {-1, 2, -1}, {2, -1, 0}}, {{0, 0, -1, 1}, {0, -1, 2, -1}, {-1, 2, -1, 0}, {2, -1, 0, 0}}, {{0, 0, 0, -1, 1}, {0, 0, -1, 2, -1}, {0, -1, 2, -1, 0}, {-1, 2, -1, 0, 0}, {2, -1, 0, 0,0}}
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FORMULA
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k=2; m(n,m,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 - 1, 0]]]], {n, 1, d}, {m, 1, d}];
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EXAMPLE
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Triangular sequence:
{1},
{1, -1},
{-1, 2, 1},
{-1, 4, 2, -1},
{1, -6, -7, 2, 1},
{1, -9, -12, 10, 2, -1},
{-1, 12, 26, -18, -13, 2, 1},
{-1, 16, 40, -52, -24,16, 2, -1},
{1, -20, -70, 86, 87, -30, -19, 2, 1}
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MATHEMATICA
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k = 2; 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 - 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: A099020 A089688 A092479 this_sequence A098063 A106396 A140998
Adjacent sequences: A124019 A124020 A124021 this_sequence A124023 A124024 A124025
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KEYWORD
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sign,tabl,uned,probation
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 31 2006
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