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A001782
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Discriminants of Shapiro polynomials.
(Formerly M5286 N2301)
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5
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Let P_0(x) = Q_0(x) = 1. For n > 0, P_{n + 1}(x) = P_n(x) + x^(2^n)*Q_n(x) and Q_{n + 1}(x) = P_n(x) - x^(2^n)*Q_n(x). Then, a(n) = discrim(P_n(x)). Note also that discrim(P_n(x)) = discrim(Q_n(x)). - Sean A. Irvine, Nov 25 2012
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PROG
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(PARI) a(n) = my(P=Pol(1), Q=1); for(i=0, n-1, [P, Q]=[P+'x^(2^i)*Q, P-'x^(2^i)*Q]); poldisc(P); \\ Kevin Ryde, Feb 23 2020
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CROSSREFS
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KEYWORD
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sign,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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