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A031358 Number of coincidence site lattices of index 4n+1 in lattice Z^2. 1
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.

LINKS

Table of n, a(n) for n=1..106.

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: A123530 A161516 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

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Last modified November 14 09:49 EST 2018. Contains 317182 sequences. (Running on oeis4.)