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A123192
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Triangle read by rows: row n gives coefficients of bracket polynomial for torus knots, p(n, x) = x*p(n - 1, x) + (-1)^(n - 1)*x^(-3*n + 2), normalized.
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0
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1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Eric Weisstein's World of Mathematics, Torus Knot
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EXAMPLE
| Triangle begins:
1
0, 0, 0, 0, -1
-1, 0, 0, 0, 0, 0, 0, 0, -1
1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1
-1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1
1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1
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MATHEMATICA
| p[0, x] = x^2; p[1, x] = -x^3; p[k_, x_] := p[k, x] = x*p[k - 1, x] + (-1)^(n - 1)*x^(-3*k + 2); w = Table[CoefficientList[x^(3*n - 2)*p[n, x], x], {n, 0, 10}]; Flatten[w]
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CROSSREFS
| Cf. A029694, A051764.
Sequence in context: A173864 A173861 A011746 * A071005 A089510 A138885
Adjacent sequences: A123189 A123190 A123191 * A123193 A123194 A123195
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KEYWORD
| tabf,sign,uned,obsc
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 03 2006
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EXTENSIONS
| Partially edited by N. J. A. Sloane (njas(AT)research.att.com), May 22 2007. The example lines suggest that these polynomials are really polynomials in x^4, in which case they should be rewritten in terms of y = x^4, which would remove most of the zero entries. Unforntunately the Mathematica code does not quite match the sequence.
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