login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.

Baake, Michael, 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 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): 711-717. [Annotated scan of page 713 only].

FORMULA

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 11 07:31 EST 2019. Contains 329914 sequences. (Running on oeis4.)