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A056498
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Number of primitive (period n) periodic palindromes using exactly two different symbols.
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3
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0, 1, 2, 3, 6, 7, 14, 18, 28, 39, 62, 81, 126, 175, 246, 360, 510, 728, 1022, 1485, 2030, 3007, 4094, 6030, 8184, 12159, 16352, 24381, 32766, 48849, 65534, 97920, 131006, 196095, 262122, 392364, 524286, 785407, 1048446, 1571310, 2097150, 3143497, 4194302, 6288381
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OFFSET
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1,3
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COMMENTS
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For example, aaabbb is not a (finite) palindrome but it is a periodic palindrome.
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} mu(k)*x^(2*k)*(1 + x^k)/((1 - x^k)*(1 - 2*x^(2*k))). - Andrew Howroyd, Sep 29 2019
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PROG
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(PARI) seq(n)={Vec(sum(k=1, n\2, moebius(k)*x^(2*k)*(1 + x^k)/((1 - x^k)*(1 - 2*x^(2*k))) + O(x*x^n)), -n)} \\ Andrew Howroyd, Sep 29 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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