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Search: id:A140885
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| A140885 |
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A coefficient triangular sequence made from the Cyclotomic polynomials, C(x,n) and their toral inverse (or reversed coefficient) polynomial x^n*C(1/x,n): p(x,n)=C[x,n]+x^n*C(1/x,n). |
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+0
1
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| 2, 2, 2, 2, 0, 2, 8, -12, -12, 8, 28, 0, -96, 0, 28, 32, 120, -160, -160, 120, 32, -56, 0, 240, 0, 240, 0, -56, 128, -1680, -1344, 3360, 3360, -1344, -1680, 128, 1936, 0, -17024, 0, 26880, 0, -17024, 0, 1936, 512, 30240, -9216, -80640, 48384, 48384, -80640, -9216, 30240, 512, -29216, 0, 279360, 0, -241920, 0
(list; table; 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:
{2, 0, 4, 6, 4, 10, 2, 14, 4, 6, 2};
All this does is make a symmetrical coefficient triangle
since the double integration is no where zero, they aren't orthogonal;
Table[Integrate[p[x, n]*p[x, m], {x, -Pi, Pi}], {n, 0, 10}, {m, 0, 10}]
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FORMULA
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p(x,n)=C[x,n]+x^n*C(1/x,n); Out_n,m=Coefficients(p(x,n)).
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EXAMPLE
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{2},
{0},
{1, 2, 1},
{1, 2, 2, 1},
{1, 0, 2, 0, 1},
{1, 2, 2, 2, 2, 1},
{1, -1, 1, 0, 1, -1, 1},
{1, 2, 2, 2, 2, 2, 2, 1},
{1, 0, 0, 0, 2, 0, 0, 0, 1},
{1, 0, 0, 2, 0, 0, 2, 0, 0, 1},
{1, -1, 1, -1, 1, 0, 1, -1, 1, -1, 1}
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MATHEMATICA
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Clear[p, x, n, m, a]; p[x_, n_] := Cyclotomic[n, x] + ExpandAll[x^n*Cyclotomic[n, 1/x]]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Cf. A013595.
Sequence in context: A065833 A097033 A113306 this_sequence A159782 A124752 A049241
Adjacent sequences: A140882 A140883 A140884 this_sequence A140886 A140887 A140888
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 22 2008
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