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A031364
Number of coincidence site modules of index 10n+1 in an icosahedral module.
2
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
OFFSET
1,4
COMMENTS
a(n) is nonzero iff n is of the form x^2+x*y+y^2 (A031363).
REFERENCES
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.
LINKS
M. Baake, Solution of the coincidence problem in dimensions d <= 4, arxiv:math/0605222 (2006), Prop. 5.4.
Michael Baake and Peter AB Pleasants, Algebraic solution of the coincidence problem in two and three dimensions, Zeitschrift für Naturforschung A 50.8 (1995): 711-717. See page 716.
Sean A. Irvine, Java program (github)
FORMULA
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
CROSSREFS
Cf. A031363.
Sequence in context: A102060 A102058 A231409 * A078473 A215833 A110800
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Missing a(8)=0 and more terms from Sean A. Irvine, Apr 29 2020
STATUS
approved