A380416 Number of corona for a diamond of edge n with diamonds of side 1.

18, 83, 258, 627, 1298, 2403, 4098, 6563, 10002

Offset: 0

Author

Craig Knecht, Jan 24 2025

Keywords

• nonn
• more

Comments

The number of diamonds that can surround a diamond(n) are the natural numbers > 2. These numbers fall into four categories: A004767(n), A004767(n) + 1, A004767(n) + 2, and A004767(n) + 3.

The number of coronal tilings for A004767(n) is 2.

The number of coronal tilings for A004767(n) + 1 is 9,25,49,81,121,169, see A016754.

The number of coronal tilings for A004767(n) + 2 is 6,40,126,288,550,936, see A089207.

The number of coronal tilings for A004767(n) + 3 is 1,16,81,256,625,1296, see A000583.

Links

• Craig Knecht, 83 corona of the D1 diamond.
• Craig Knecht, Coronal Reptile.
• Craig Knecht, Example for the sequence.
• Craig Knecht, Feihu Liu, and Guoce Xin, Enumeration of Corona for Lozenge Tilings, arXiv:2504.19269 [math.CO], 2025.

Crossrefs

Cf. A000583, A004767, A016754, A089207, A380346.