The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A145390 Number of sublattices of index n of a centered rectangular lattice fixed by a reflection. 6
 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; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is the Dirichlet convolution of A000012 and A098178. - Domenico (domenicoo(AT)gmail.com), Oct 21 2009 LINKS Andrey Zabolotskiy, Table of n, a(n) for n = 1..10000 Amihay Hanany, Domenico Orlando, and Susanne Reffert, Sublattice counting and orbifolds, High Energ. Phys., 2010 (2010), 51, arXiv.org:1002.2981 [hep-th] (see Table 3) 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]. - From N. J. A. Sloane, Feb 23 2009 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). - Domenico (domenicoo(AT)gmail.com), Oct 21 2009 If 4|n then a(n) = d(n) - d(n/2) + 2*d(n/4); else if 2|n then a(n) = d(n) - d(n/2); else a(n) = d(n); where d(n) is the number of divisors of n. [Rutherford] - Andrey Zabolotskiy, Mar 10 2018 a(n) = Sum_{ m: m^2|n } A060594(n/m^2). - Andrey Zabolotskiy, May 07 2018 Sum_{k=1..n} a(k) ~ n*(log(n) - 1 + 2*gamma - log(2)/2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 02 2019 MAPLE nmax := 100 : L := [1, -1, 0, 2, seq(0, i=1..nmax)] : MOBIUSi(%) : MOBIUSi(%) ; # R. J. Mathar, Sep 25 2017 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] (* Jean-François Alcover, Sep 20 2011, after formula *) 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) CROSSREFS Cf. A098178, A060594 (primitive sublattices only), A145391. Sequence in context: A286529 A306225 A077199 * A270026 A128049 A104543 Adjacent sequences:  A145387 A145388 A145389 * A145391 A145392 A145393 KEYWORD nonn,mult AUTHOR N. J. A. Sloane, Feb 23 2009, Mar 13 2009 EXTENSIONS New name from Andrey Zabolotskiy, Mar 10 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)