|
Search: id:A145390
|
|
|
| A145390 |
|
Number of sublattices of index n fixed by a certain point group (see reference for precise definition). |
|
+0
4
|
|
| 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; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
a(n) is the Dirichlet convolution of 1 and A098178 [From Domenico (domenicoo(AT)gmail.com), Oct 21 2009]
|
|
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, 156163. [See Table 1].
|
|
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]
|
|
PROGRAM
|
(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)
|
|
CROSSREFS
|
Sequence in context: A147561 A103266 A072814 this_sequence A128049 A104543 A054988
Adjacent sequences: A145387 A145388 A145389 this_sequence A145391 A145392 A145393
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Feb 23 2009, Mar 13 2009
|
|
|
Search completed in 0.002 seconds
|
