OFFSET
1,65
COMMENTS
From Andrey Zabolotskiy, May 09 2018: (Start)
Also, the number of partitions of n into 2 distinct coprime squares.
All such sublattices (including non-primitive ones) are counted in A025441.
The primitive sublattices that have the same symmetries (including the orientation of the mirrors) as the parent lattice are not counted here; they are counted in A019590, and all such sublattices (including non-primitive ones) are counted in A053866.
For n > 2, equals A193138. (End)
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
a(n) = 1 if n>2 is in A224450, a(n) = 2 if n is in A224770, a(n) is a higher power of 2 if n is in A281877 (first time reaches 8 at n = 32045). - Andrey Zabolotskiy, Sep 30 2018
a(n) = b(n) for odd n, a(n) = b(n/2) for even n, where b(n) = A024362(n). - Andrey Zabolotskiy, Jan 23 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 25 2009
EXTENSIONS
New name and more terms from Andrey Zabolotskiy, May 09 2018
STATUS
approved