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A140885
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Triangle T(n,k) read by rows: the coefficient [x^k] ( Phi(n,x)+x^n*Phi(n,1/x)) related to cyclotomic polynomials Phi(n,x).
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0
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0, 0, 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, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, -1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are: 0, 0, 4, 6, 4, 10, 2, 14, 4, 6, 2, 22, 2, 26, 2, 2, 4, 34, 2, 38, 2,...
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FORMULA
| T(n,k) = T(n,n-k) .
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EXAMPLE
| 0; # x+x^0*(1/x) = x+1/x
0, 0; # x-1+x*(1/x-1) = 0
1, 2, 1; # x+1+x^2*(1/x+1) = 1+2*x+x^2
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
| 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
| Cf. A013595.
Sequence in context: A171533 A115236 A190672 * A064286 A002471 A091243
Adjacent sequences: A140882 A140883 A140884 * A140886 A140887 A140888
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KEYWORD
| tabl,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 22 2008
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EXTENSIONS
| All entries replaced to comply with the definition and examples - The Assoc. Eds. of the OEIS, Oct 12 2010
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