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A031364
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Number of coincidence site modules of index 10n+1 in an icosahedral module.
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2
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1, 0, 0, 5, 6, 0, 0, 0, 10, 0, 24, 0, 0, 0, 0, 20, 0, 0, 40, 30, 0, 0, 0, 0, 30, 0, 0, 0, 60, 0, 64, 0, 0, 0, 0, 50, 0, 0, 0, 0, 84, 0, 0, 120, 60, 0, 0, 0, 50, 0, 0, 0, 0, 0, 144, 0, 0, 0, 120, 0, 124, 0, 0, 80, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 200, 0, 0
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OFFSET
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1,4
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COMMENTS
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a(n) is nonzero iff n is of the form x^2+x*y+y^2 (A031363).
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REFERENCES
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Michael Baake, "Solution of coincidence problem in dimensions d<=4", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.
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LINKS
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FORMULA
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Dirichlet series: ((1+5^(-s))/(1-5^(1-s))) * Product_{p = +-2 (mod 5)} ((1+p^(-2*s))/(1-p^(2*(1-s)))) * Product_{p = +-1 (mod 5)} ((1+p^(-s))/(1-p^(1-s)))^2. - Sean A. Irvine, Apr 29 2020
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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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EXTENSIONS
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STATUS
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approved
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