Search: id:A145390
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%I A145390
%S A145390 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,
%T A145390 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,
%U A145390 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
%N A145390 Number of sublattices of index n fixed by a certain point group (see 
               reference for precise definition).
%C A145390 a(n) is the Dirichlet convolution of 1 and A098178 [From Domenico (domenicoo(AT)gmail.com), 
               Oct 21 2009]
%D A145390 John S. Rutherford, Sublattice enumeration. IV. Equivalence classes of 
               plane sublattices by parent Patterson symmetry and colour lattice 
               group type, Acta Cryst. (2009). A65, 156163. [See Table 1].
%F A145390 Dirichlet g.f.: (1-2^(-s)+2*4^(-s))*zeta^2(s).
%F A145390 g.f. \sum_n ( (1 + \cos(n \pi /2)) x^n ) / (1 - x^n) [From Domenico (domenicoo(AT)gmail.com), 
               Oct 21 2009]
%o A145390 (PARI) t1=direuler(p=2,200,1/(1-X)^2)
%o A145390 t2=direuler(p=2,2,1-X+2*X^2,200)
%o A145390 t3=dirmul(t1,t2)
%Y A145390 Sequence in context: A147561 A103266 A072814 this_sequence A128049 A104543 
               A054988
%Y A145390 Adjacent sequences: A145387 A145388 A145389 this_sequence A145391 A145392 
               A145393
%K A145390 nonn
%O A145390 1,3
%A A145390 N. J. A. Sloane (njas(AT)research.att.com), Feb 23 2009, Mar 13 2009

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