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

0,1

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

Table of n, a(n) for n=0..8.

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.

Sequence in context: A043961 A067984 A372400 * A281372 A124935 A126405

Adjacent sequences: A380413 A380414 A380415 * A380417 A380418 A380419

Keyword

nonn,more

Author

Craig Knecht, Jan 24 2025

Status

approved