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Search: id:A051047
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| A051047 |
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For definition see Mathematica code. |
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+0
4
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| 1, 3, 8, 120, 1680, 23408, 326040, 4541160, 63250208, 880961760, 12270214440, 170902040408, 2380358351280, 33154114877520, 461777249934008, 6431727384198600, 89582406128846400, 1247721958419651008
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The recurrence gives an infinite sequence of polynomials S={x,x+2,c_1(x),c_2(x),...} such that the product of any two consecutive polynomials, increased by 1, is the square of a polynomial - see the Jones reference.
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REFERENCES
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Jones, B. W. "A Variation of a Problem of Davenport and Diophantus." Quart. J. Math. (Oxford) Ser. (2) 27, 349-353, 1976.
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LINKS
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Andrej Dujella and Attila Petho, Generalization of a theorem of Baker and Davenport [From William Stein, Oct 24 2009]
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MATHEMATICA
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With[{x = 1},
Join[{x, x + 2},
RecurrenceTable[{c[-1] == c[0] == 0,
c[k] == (4 x^2 + 8 x + 2) c[k - 1] - c[k - 2] + 4 (x + 1)}, c, {k, 1, 12}]]]
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CROSSREFS
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Cf. A051048. Essentially the same as A045899.
Sequence in context: A123279 A134803 A030063 this_sequence A036504 A132491 A083112
Adjacent sequences: A051044 A051045 A051046 this_sequence A051048 A051049 A051050
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Entry revised by N. J. A. Sloane, Oct 25 2009, following correspondence with Eric Weisstein
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