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Search: id:A137349
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| A137349 |
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A triangular sequence from coefficients of a mixed type of three deep polynomial recursion: Q(x, n) = 6*x*Q(x, n - 2)*Q(x, n - 3) - 2*Q(x, n - 3). |
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+0
1
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| 1, -2, 2, 0, -2, -12, 12, 4, -4, 0, 4, -24, -264, 576, -288, -8, 8, 0, -8, -144, 1872, 10368, -39744, 41472, -13824, 16, -16
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:
{1, 0, 0, -2, 0, 0, 4, 0, 0, -8, 0}
This polynomial recursion was suggested by the soliton equation ( Korteweg and de Vries) in McKean and Moll, but is my own idea.
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REFERENCES
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McKean and Moll, Ellipic Curves, Function Theory,Geometry, Arithmetic, Cambridge University Press, New York, 1997, page 91
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FORMULA
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Q(x, n) = 6*x*Q(x, n - 2)*Q(x, n - 3) - 2*Q(x, n - 3).
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EXAMPLE
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{1},
{-2, 2},
{0},
{-2, -12, 12},
{4, -4},
{0},
{4, -24, -264, 576, -288},
{-8, 8},
{0},
{-8, -144, 1872, 10368, -39744, 41472, -13824},
{16, -16}
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MATHEMATICA
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Clear[Q, x] Q[x, -2] = 1 - x; Q[x, -1] = 0; Q[x, 0] = 1; Q[x_, n_] := Q[x, n] = 6*x*Q[x, n - 2]*Q[x, n - 3] - 2*Q[x, n - 3] Table[ExpandAll[Q[x, n]], {n, 0, 10}] a = Table[CoefficientList[Q[x, n], x], {n, 0, 10}] (* here I had to add {0} for null {} to get a representation*) Flatten[{{1}, {-2, 2}, {0}, {-2, -12, 12}, {4, -4}, {0}, {4, -24, -264, 576, -288}, {-8, 8}, {0}, {-8, -144, 1872, 10368, -39744, 41472, -13824}, {16, -16}}]
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CROSSREFS
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Adjacent sequences: A137346 A137347 A137348 this_sequence A137350 A137351 A137352
Sequence in context: A052422 A011218 A028305 this_sequence A087318 A087319 A101348
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2008
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