

A031358


Number of coincidence site lattices of index 4n+1 in lattice Z^2.


3



1, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 2, 0, 0, 4, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, 2, 4, 0, 2, 2, 0, 4, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2
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OFFSET

1,2


REFERENCES

M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of LongRange Aperiodic Order, Kluwer 1997, pp. 944.
Baake, Michael, and Peter AB Pleasants. "Algebraic solution of the coincidence problem in two and three dimensions." Zeitschrift für Naturforschung A 50.8 (1995): 711717. See page 713.


LINKS

Table of n, a(n) for n=1..106.
Baake, Michael, and Peter AB Pleasants, Algebraic solution of the coincidence problem in two and three dimensions, Zeitschrift für Naturforschung A 50.8 (1995): 711717. [Annotated scan of page 713 only].


FORMULA

Dirichlet series: Product_{primes p == 1 mod 4} (1+p^(s))/(1p^(s)).


PROG

(PARI) t1=direuler(p=2, 1200, (1+(p%4<2)*X))
t2=direuler(p=2, 1200, 1/(1(p%4<2)*X))
t3=dirmul(t1, t2)
t4=vector(200, n, t3[4*n+1]) (and then prepend 1)


CROSSREFS

Cf. A175647.
Sequence in context: A161516 A329491 A123063 * A279103 A318734 A029317
Adjacent sequences: A031355 A031356 A031357 * A031359 A031360 A031361


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from N. J. A. Sloane, Mar 13 2009
Added condition that p must be prime to the Dirichlet series.  N. J. A. Sloane, May 26 2014


STATUS

approved



