A031364 Number of coincidence site modules of index 10n+1 in an icosahedral module.
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
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)
Crossrefs
Cf. A031363.
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
Extensions
Missing a(8)=0 and more terms from Sean A. Irvine, Apr 29 2020
Comments