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A137289
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Triangle of coefficients of Boubaker polynomials.
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2
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1, 2, 1, -2, 0, 1, 2, -3, -2, 1, -2, 8, 0, -4, 1, 2, -15, 10, 7, -6, 1, -2, 24, -35, 0, 18, -8, 1, 2, -35, 84, -42, -30, 33, -10, 1, -2, 48, -168, 168, 0, -88, 52, -12, 1, 2, -63, 300, -462, 198, 143, -182, 75, -14, 1, -2, 80, -495, 1056, -858, 0, 455, -320, 102, -16, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This was suggested by a set of polynomials in one of Karem Boubaker's papers.
Row sums repeat in magnitude:
Table[Apply[Plus, CoefficientList[B[x, n] /. x -> Sqrt[y], y]], {n, 0, 20, 2}];
{1, 3, -1, -2, 3, -1, -2, 3, -1, -2, 3, ...}.
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REFERENCES
| Hedi Labiadh and Karem Boubaker, "A Sturm-Loiville shaped characteristic differential equation as a guide to establish a quasi-polynomial expression to the Boubaker polynomials" Differential Equations and Control Processes, #2,2007, ISSN 1817-2172
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FORMULA
| B(x, n) = x*B(x, n - 1) - B(x, n - 2); p(y,n)=B[Sqrt[y],2*n)
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EXAMPLE
| {1},
{2, 1},
{-2, 0, 1},
{2, -3, -2, 1},
{-2, 8, 0, -4, 1},
{2, -15, 10, 7, -6, 1},
{-2, 24, -35, 0, 18, -8, 1},
{2, -35, 84, -42, -30, 33, -10, 1},
{-2, 48, -168, 168,0, -88, 52, -12, 1},
{2, -63, 300, -462, 198, 143, -182, 75, -14,1},
{-2, 80, -495, 1056, -858, 0, 455, -320, 102, -16, 1}
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MATHEMATICA
| Clear[B, a] B[x, 0] = 1; B[x, 1] = x; B[x, 2] = 2 + x^2; B[x, 4] = -2 + x^4; B[ x, 3] = x + x^3; B[x_, n_] := B[x, n] = x*B[x, n - 1] - B[x, n - 2]; a = Table[CoefficientList[B[x, n] /. x -> Sqrt[y], y], {n, 0, 20, 2}]; Flatten[a]
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CROSSREFS
| Cf. A135929, A138034.
Sequence in context: A114002 A114004 A049986 * A063574 A144515 A178650
Adjacent sequences: A137286 A137287 A137288 * A137290 A137291 A137292
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KEYWORD
| sign,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 14 2008
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 05 2009
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