A141682 Number of isomorphism classes of (2n+1)-reflexive polygons.

16, 1, 12, 29, 1, 61, 81, 1, 113, 131, 2, 163, 50, 2, 215, 233, 2, 34, 285, 3, 317, 335, 2, 367, 182, 3, 419, 72, 4, 469, 489, 3, 93, 539, 4, 571, 591, 3, 185, 641, 5, 673, 131, 5, 725, 240, 6, 148, 795, 5, 827, 845, 3, 877, 897, 7, 929, 186, 6, 338, 656, 7, 240, 1049, 8, 1081, 393, 5, 1133, 1151, 8, 542, 245, 7, 1235, 1253

Offset: 0

Author

Benjamin Nill, Jul 02 2012

Keywords

• nonn

Comments

There are no l-reflexive polygons for even index l.

Examples

			a(0)=16 equals the number of isomorphism classes of (1-)reflexive polygons, A090045(2).
		

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 0..99 (from the Graded Ring Database)
• Dimitrios I. Dais, On the Twelve-Point Theorem for l-Reflexive Polygons, arXiv:1806.08351 [math.CO], 2018.
• A. M. Kasprzyk and B. Nill, Reflexive polytopes of higher index and the number 12, arXiv:1107.4945 [math.AG], 2011.
• A. M. Kasprzyk and B. Nill, Toric l-reflexive surfaces at Graded Ring Database.

Crossrefs

Cf. A090045.

Formula

It seems that for n > 2, a(n) = 17*n - k where k = 21, 22, 23, 24 iff 2*n+1 is a prime from A068228, A068229, A040117, A068231, respectively. - Andrey Zabolotskiy, Apr 21 2022