A056844 Number of polydiamonds: polyforms made from n diamonds.

1, 2, 9, 40, 238, 1518, 10276, 71528, 507725, 3650323, 26511768

Offset: 1

Author

James Sellers, Aug 28 2000

Keywords

• nice
• nonn
• more
• hard

Comments

If you look at Vicher's picture of the 40 4-celled polydiamonds (link below), near the middle of the picture is a polydiamond that looks like the traditional 2-D representation of a cube with an extra diamond stuck to the edge. Depending on how you orient the cube, there are actually 2 different ways to form this polydiamond, although there is no change in the perimeter shape. - Larry_Reeves(AT)intranetsolutions.com, Jun 22 2001; edited by Aaron N. Siegel, May 18 2022

From Aaron N. Siegel, May 18 2022: (Start)

The polydiamonds of order n form a subset of the polyiamonds of order 2n. In particular, the polydiamonds of order n are exactly the polyiamonds of order 2n that admit at least one tiling by diamonds.

Two polydiamonds are considered distinct only if their perimeter shapes are different (equivalently, if they represent distinct 2n-iamonds); the internal division into diamonds is not significant. This distinguishes A056844 from the related sequence A056845. The two sequences first diverge at n = 4.

(End)

Links

• Abaroth's World, Polydiamonds
• M. Vicher, Polyforms
• M. Vicher, The 40 4-celled polydiamonds
• M. Vicher, The 40 4-celled polydiamonds

Crossrefs

Cf. A056845, A056785, A056786.

Extensions

Edited by N. J. A. Sloane, Jun 21 2001

a(6) corrected and a(7)-a(11) from Aaron N. Siegel, May 17 2022