cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A038587 Sizes of successive clusters in hexagonal lattice A_2 centered at deep hole.

Original entry on oeis.org

3, 6, 12, 12, 18, 21, 27, 27, 30, 36, 42, 42, 48, 48, 54, 54, 63, 69, 69, 69, 75, 78, 84, 84, 90, 96, 102, 102, 102, 102, 114, 114, 120, 123, 129, 129, 135, 141, 141, 141, 144, 150, 156, 156, 168, 168, 174, 174, 174
Offset: 0

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Author

N. J. A. Sloane

Keywords

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

Links

Crossrefs

Partial sums of A005882.
Cf. A038588.

Programs

  • Mathematica
    CoefficientList[3 QPochhammer[q^3]^3 / QPochhammer[q] + O[q]^50, q] // Accumulate (* Jean-François Alcover, Jul 05 2019 *)

A038591 Sizes of clusters in hexagonal lattice A_2 with 3-fold symmetry.

Original entry on oeis.org

1, 3, 6, 7, 12, 13, 18, 19, 21, 27, 30, 31, 36, 37, 42, 43, 48, 54, 55, 61, 63, 69, 73, 75, 78, 84, 85, 90, 91, 96, 97, 102, 109, 114, 120, 121, 123, 127, 129, 135, 139, 141, 144, 150, 151, 156, 163, 168, 169, 174, 180
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

Links

Crossrefs

Union of A038588 and A038590.

A240600 Number of partially filled hexagons in the first 120-degree circular sector of hexagonal lattice A_2 centered at deep hole along the edge of a circle also centered at the deep hole.

Original entry on oeis.org

0, 1, 1, 2, 2, 4, 3, 3, 3, 5, 4, 5, 5, 7, 5, 5, 5, 6, 6, 8, 6, 8, 7, 7, 7, 9, 7, 7, 7, 9, 8, 9, 9, 11, 9, 11, 9, 9, 9, 11, 9, 10, 10, 12, 10, 12, 12, 14, 12, 14, 13, 13, 11, 11, 11, 13, 13, 15, 13, 13, 13, 15, 14
Offset: 0

Views

Author

Rajan Murthy, Apr 09 2014

Keywords

Comments

A(n) alternates between the numbers for circles which intersect points on the A2 lattice and the numbers for circles which pass in between the points on a lattice.

Examples

			for n = 1, the squared radius is in the open interval (0,1) and the corresponding circle passes through 1 hexagon.
for n = 14, the squared radius is 13 with the corresponding circle passing through the furthest corner of 2 hexagons and passing through 5 hexagons.

Links

Crossrefs

A038588 gives the number of hexagons completely encircled in all three circular sectors.
Squared radii of alternate entries is given by the Loeschian numbers A003136.
A234300 is the analog for the 2-d Cartesian lattice.
A237708 is the analog for the 3-d Cartesian lattice.
A239353 is the analog for the 4-d Cartesian lattice.

A240692 Squared radii of circles which exactly encircle clusters in the A2 lattice in increasing order.

Original entry on oeis.org

0, 4, 9, 13, 21, 25, 28, 36, 39, 43, 49, 57, 63, 64, 67, 76, 81, 84, 91, 93, 97, 109, 111, 117, 121, 124, 129, 133, 144, 147, 148, 156, 157, 163, 171, 175, 183, 189, 193, 196, 199, 201
Offset: 0

Views

Author

Rajan Murthy, Apr 10 2014

Keywords

Examples

			For n = 1, a(1) = 4, the squared distance to the corners furthest from the deep hole of three hexagons which share the deep hole as a corner.
For n= 3, a(3) = 13, the squared distance to the furthest corners of the 6 hexagons third most distant from the deep hole - which, when added to the 3 that are closest and the 3 that are second-closest, yields a total of 12, which is A038588(3).

Links

Crossrefs

A038588(n) gives the corresponding cluster size starting at n = 1 (the first positive radius circle);
A000404 is the analog for a Cartesian lattice.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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