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Search: id:A144473
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| A144473 |
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A triangle sequence of determinants: a(n)=If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 0]]]; b(n,m)=If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M={{a(m), b(n, m)}, {a(n), b(n, n)}}; t(n,m)=Det[M]. |
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+0
1
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| -1, -1, 1, -1, 1, 0, -1, 1, 0, -1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are:{-1, 0, 0, -1, 0, 0, -1, 0, 0, -1}.
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FORMULA
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a(n)=If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 0]]]; b(n,m)=If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M={{a(m), b(n, m)}, {a(n), b(n, n)}}; t(n,m)=Det[M].
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EXAMPLE
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{-1},
{-1, 1},
{-1, 1, 0},
{-1, 1, 0, -1},
{-1, 1, 0, -1, 1},
{-1, 1, 0, -1, 1, 0},
{-1, 1, 0, -1, 1, 0, -1},
{-1, 1, 0, -1, 1, 0, -1, 1},
{-1, 1, 0, -1, 1, 0, -1, 1, 0},
{-1, 1, 0, -1, 1, 0, -1, 1, 0, -1}
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MATHEMATICA
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Clear[a, b, t, n, m] a[n_] := If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 0]]]; b[n, m_] := If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M := {{a[m], b[n, m]}, {a[n], b[n, n]}}; t[n_, m_] := Det[M]; Table[Table[t[n, m], {m, 0, n - 1}], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A140653 A118110 A131522 this_sequence A011750 A010055 A076699
Adjacent sequences: A144470 A144471 A144472 this_sequence A144474 A144475 A144476
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 10 2008
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