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!)
 A157226 Number of primitive inequivalent sublattices of square lattice having mirrors parallel to the sides of the unit cell of the parent lattice of index n. 6
 0, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 4, 1, 3, 2, 2, 1, 3, 1, 4, 2, 3, 1, 4, 1, 3, 1, 4, 1, 6, 1, 2, 2, 3, 2, 4, 1, 3, 2, 4, 1, 6, 1, 4, 2, 3, 1, 4, 1, 3, 2, 4, 1, 3, 2, 4, 2, 3, 1, 8, 1, 3, 2, 2, 2, 6, 1, 4, 2, 6, 1, 4, 1, 3, 2, 4, 2, 6, 1, 4, 1, 3, 1, 8, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Andrey Zabolotskiy's new formula confirms that a(n) indeed is a function of A305891(n). - Antti Karttunen, Oct 01 2018 LINKS Andrey Zabolotskiy, Table of n, a(n) for n = 1..5000 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 5.] FORMULA From Andrey Zabolotskiy, Sep 30 2018: (Start) Let b(n) = A007875(n) for n>1, b(1) = 0. Then a(n) = b(n) for odd n, a(n) = b(n) + b(n/2) for even n. Thus the sorted list of all terms (except for a(1)=0) is A029744. (End) PROG (PARI) A007875(n) = eulerphi(2^omega(n)); A157226(n) = if(n<=2, n-1, (A007875(n) + if(!(n%2), A007875(n/2)))); \\ Antti Karttunen, Oct 01 2018 CROSSREFS Cf. A145393 (all sublattices of the square lattice), A019590, A157228, A157230, A157231, A304182, A007875, A029744. Sequence in context: A108103 A111376 A241664 * A156249 A187808 A317673 Adjacent sequences:  A157223 A157224 A157225 * A157227 A157228 A157229 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 25 2009 EXTENSIONS New name and more terms from Andrey Zabolotskiy, May 09 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 May 11 13:41 EDT 2021. Contains 343791 sequences. (Running on oeis4.)