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A145390
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Number of sublattices of index n fixed by a certain point group (see reference for precise definition).
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3
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1, 1, 2, 3, 2, 2, 2, 5, 3, 2, 2, 6, 2, 2, 4, 7, 2, 3, 2, 6, 4, 2, 2, 10, 3, 2, 4, 6, 2, 4, 2, 9, 4, 2, 4, 9, 2, 2, 4, 10, 2, 4, 2, 6, 6, 2, 2, 14, 3, 3, 4, 6, 2, 4, 4, 10, 4, 2, 2, 12, 2, 2, 6, 11, 4, 4, 2, 6, 4, 4, 2, 15, 2, 2, 6, 6, 4, 4, 2, 14, 5, 2, 2, 12, 4, 2, 4, 10, 2, 6, 4, 6, 4, 2, 4, 18, 2, 3, 6, 9, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) is the Dirichlet convolution of A000012 and A098178 [From Domenico (domenicoo(AT)gmail.com), Oct 21 2009]
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REFERENCES
| John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type, Acta Cryst. (2009). A65, 156-163. [See Table 1].
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LINKS
| John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type, Acta Cryst. A65 (2) (2009) 156-163. [See Table 1].
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FORMULA
| Dirichlet g.f.: (1-2^(-s)+2*4^(-s))*zeta^2(s).
g.f. sum_n (1 + \cos(n*Pi/2)) x^n / (1 - x^n) [From Domenico (domenicoo(AT)gmail.com), Oct 21 2009]
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MATHEMATICA
| m = 101; Drop[ CoefficientList[ Series[ Sum[(1 + Cos[n*Pi/2])*x^n/(1 - x^n), {n, 1, m}], {x, 0, m}], x], 1] (* From Jean-François Alcover, Sep 20 2011, after formula *)
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PROG
| (PARI) t1=direuler(p=2, 200, 1/(1-X)^2)
t2=direuler(p=2, 2, 1-X+2*X^2, 200)
t3=dirmul(t1, t2)
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CROSSREFS
| Sequence in context: A103266 A072814 A205717 * A128049 A104543 A054988
Adjacent sequences: A145387 A145388 A145389 * A145391 A145392 A145393
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KEYWORD
| nonn,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 23 2009, Mar 13 2009
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