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A031358 Number of coincidence site lattices of index 4n+1 in lattice Z^2. 4
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
0,2
LINKS
M. Baake, Solution of the coincidence problem in dimensions d <= 4, in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44; arXiv:math/0605222 [math.MG], 2006.
Michael Baake and Peter A. B. Pleasants, Algebraic solution of the coincidence problem in two and three dimensions, Zeitschrift für Naturforschung A 50.8 (1995): 711-717. See annotated scan of page 713.
FORMULA
Dirichlet series: Product_{primes p == 1 mod 4} (1+p^(-s))/(1-p^(-s)).
a(n) = 2*A106594(n) for n > 0. - Andrey Zabolotskiy, Jan 30 2020
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, A031359, A331140, A106594, A094178 (positions of nonzero terms).
Sequence in context: A347730 A329491 A123063 * A279103 A318734 A029317
KEYWORD
nonn,easy,nice
AUTHOR
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
Offset corrected by Andrey Zabolotskiy, Jan 30 2020
STATUS
approved

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Last modified June 23 03:01 EDT 2024. Contains 373629 sequences. (Running on oeis4.)