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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Missing a(8)=0 and more terms from Sean A. Irvine, Apr 29 2020
STATUS
approved