A380346 Number of corona for a hexagon of edge n with diamonds of side 1.

18, 198, 1298, 5778, 19602, 54758, 132498, 287298, 571538, 1060902

Offset

0,1

Comments

The number of diamonds that can surround a hexagon(n) fall into four categories: A016945(n), A016945(n) + 1, A016945(n) + 2, and A016945(n) + 3.

The number of coronal tilings for A016945(n) is 2.

The number of coronal tilings for A016945(n) + 1 is 9,36,81,144,225, see A016766.

The number of coronal tilings for A016945(n) + 2 is 6,96,486,1536,3750,7776,14406 = 6*A000583.

The number of coronal tilings for A016945(n) + 3 is 1,64,729,4096,15625, see A001014.

A008793 looks at the enumeration of diamonds inside the hexagon. In contrast this looks at the enumeration of diamond cornona of the hexagon.

Links

Table of n, a(n) for n=0..9.

Craig Knecht, 198 diamond corona of the H1 hexagon.

Craig Knecht, Example for the sequence.

Craig Knecht, H1 corona sorted by the number of coronal tiles.

Craig Knecht, Hexagon diamond corona inside a hexagon diamond tiling.

Formula

a(n) = n^6 + 6*n^5 + 21*n^4 + 44*n^3 + 60*n^2 + 48*n + 18 (conjectured).

Crossrefs

Cf. A001014, A008793, A016766, A016945, A380416.

Sequence in context: A042940 A264356 A034727 * A060532 A073397 A020920

Adjacent sequences: A380343 A380344 A380345 * A380347 A380348 A380349

Keyword

nonn,more

Author

Craig Knecht, Jan 22 2025

Status

approved