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A144474
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A triangle sequence of determinants: a(n)=If[Mod[n, 2] == 0, 1, If[Mod[n, 2] == 1, -1, 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
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-1, -2, 0, -1, 1, -1, -1, 1, -1, 1, -2, 0, -2, 0, -2, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -2, 0, -2, 0, -2, 0, -2, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums are:{-1, -2, -1, 0, -6, 0, -1, -8, -1, 0}.
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FORMULA
| a(n)=If[Mod[n, 2] == 0, 1, If[Mod[n, 2] == 1, -1, 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
| {-1},
{-2, 0},
{-1, 1, -1},
{-1, 1, -1, 1},
{-2, 0, -2, 0, -2},
{-1, 1, -1, 1, -1, 1},
{-1, 1, -1, 1, -1, 1, -1},
{-2, 0, -2, 0, -2, 0, -2, 0},
{-1, 1, -1, 1, -1, 1, -1, 1, -1},
{-1, 1, -1, 1, -1, 1, -1, 1, -1, 1}
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MATHEMATICA
| Clear[a, b, t, n, m] a[n_] := If[Mod[n, 2] == 0, 1, If[Mod[n, 2] == 1, -1, 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
| Sequence in context: A194301 A194341 A171905 * A203949 A070200 A025914
Adjacent sequences: A144471 A144472 A144473 * A144475 A144476 A144477
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KEYWORD
| sign,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 10 2008
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