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Search: id:A123192
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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
1
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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; listen)
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Torus Knot
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EXAMPLE
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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
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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
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Cf. A029694, A051764.
Sequence in context: A027356 A097080 A011746 this_sequence A089510 A138885 A014065
Adjacent sequences: A123189 A123190 A123191 this_sequence A123193 A123194 A123195
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KEYWORD
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tabf,sign,uned,obsc
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 03 2006
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EXTENSIONS
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Partially edited by njas, 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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