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A271494
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Expansion of (1+16*x)/((1+4*x)*(1-8*x)).
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4
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1, 20, 112, 1088, 7936, 66560, 520192, 4210688, 33488896, 268697600, 2146435072, 17184063488, 137422176256, 1099578736640, 8795824586752, 70369817919488, 562945658454016, 4503616807239680, 36028728299487232, 288230651029618688, 2305841909702066176, 18446748471756062720
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OFFSET
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0,2
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COMMENTS
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Sixth moments of the Rudin-Shapiro polynomials.
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REFERENCES
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Shalosh B. Ekhad, Explicit Generating Functions, Asymptotics, and More for the First 10 Even Moments of the Rudin-Shapiro Polynomials, Preprint, 2016.
Doron Zeilberger, Personal Communication to N. J. A. Sloane, Apr 15 2016.
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LINKS
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FORMULA
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a(n) = 2^(1+3*n)-(-4)^n.
a(n) = 4*a(n-1) + 32*a(n-2) for n>1.
(End)
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MATHEMATICA
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CoefficientList[Series[(1+16x)/((1+4x)(1-8x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 32}, {1, 20}, 30] (* Harvey P. Dale, May 13 2017 *)
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PROG
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(PARI) Vec((1+16*x)/((1+4*x)*(1-8*x)) + O(x^50)) \\ Colin Barker, Apr 17 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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