A346784 Numerators of minimal squared radii of circular disks covering a record number of lattice points of the hexagonal lattice, when the centers of the circles are chosen to maximize the number of covered lattice points.

0, 1, 1, 3, 1, 7, 49, 9, 7, 13, 169, 91, 4, 133, 21, 361, 1729, 169, 19, 7, 961, 133, 9, 39, 21793, 481, 31, 9331, 301, 3367, 49, 817, 13, 361, 931, 1813, 63, 16

Offset

1,4

Comments

It is conjectured that the number of covered grid points is given by A346126(n-1) for n>2.

Links

Table of n, a(n) for n=1..38.

Hugo Pfoertner, Examples of self avoiding walks of minimum diameter on the hexagonal lattice.

Example

0, 1/4, 1/3, 3/4, 1, 7/4, 49/25, 9/4, 7/3, 13/4, 169/48, 91/25, 4, 133/27, 21/4, 361/64, 1729/289, 169/27, 19/3, 7, 961/121, 133/16, 9, 39/4, 21793/2187, ...
.
     Diameter  Covered      R^2 =
     of disk   grid        (D/2)^2 =
   n    D      points    a(n) / A346785(n)
.
   1 0.00000     1        0   /    1
   2 1.00000     2        1   /    4
   3 1.15470     3        1   /    3
   4 1.73205     4        3   /    4
   5 2.00000     7        1   /    1
   6 2.64575     8        7   /    4
   7 2.80000     9       49   /   25
   8 3.00000    10        9   /    4
   9 3.05505    12        7   /    3
  10 3.60555    14       13   /    4

Crossrefs

Corresponding denominators are A346785.

Cf. A125852, A346126.

Sequence in context: A282422 A282685 A194583 * A060487 A285020 A165781

Adjacent sequences: A346781 A346782 A346783 * A346785 A346786 A346787

Keyword

nonn,frac,more

Author

Hugo Pfoertner, Aug 08 2021

Status

approved