cp's OEIS Frontend

A056844 Number of polydiamonds: polyforms made from n diamonds.

%I A056844 #41 Jul 02 2025 16:02:00
%S A056844 1,2,9,40,238,1518,10276,71528,507725,3650323,26511768
%N A056844 Number of polydiamonds: polyforms made from n diamonds.
%C A056844 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
%C A056844 From _Aaron N. Siegel_, May 18 2022: (Start)
%C A056844 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.
%C A056844 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.
%C A056844 (End)
%H A056844 Abaroth's World, <a href="https://abarothsworld.com/Puzzles/Polyiamonds/Polydiamonds.htm">Polydiamonds</a>
%H A056844 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%H A056844 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyform/comp/images/diam2.gif">The 40 4-celled polydiamonds</a>
%H A056844 M. Vicher, <a href="/A056844/a056844.gif">The 40 4-celled polydiamonds</a>
%Y A056844 Cf. A056845, A056785, A056786.
%K A056844 nice,nonn,more,hard
%O A056844 1,2
%A A056844 _James Sellers_, Aug 28 2000
%E A056844 Edited by _N. J. A. Sloane_, Jun 21 2001
%E A056844 a(6) corrected and a(7)-a(11) from _Aaron N. Siegel_, May 17 2022