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%I #30 Jul 18 2022 19:14:15
%S 1,2,9,41,248,1610,11065,78218,563675,4113988,30329616,225394071,
%T 1686227909
%N Number of distinct connected planar figures that can be formed from n non-overlapping diamonds.
%C If you look at Vicher's picture of the 40 4-celled polydiamonds (link in A056844), 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 Two figures are considered distinct even if their perimeter shapes are identical, provided their internal arrangements of diamonds are distinct (and not related by symmetry). This distinguishes the related sequence A056844 from A056845. The two sequences first diverge at n = 4. - _Aaron N. Siegel_, May 18 2022
%H M. Keller, <a href="http://www.solitairelaboratory.com/polyenum.html">More information</a>
%H M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%Y Cf. A056844, A056785, A056786.
%K nonn,more,hard
%O 1,2
%A _James A. Sellers_, Aug 28 2000
%E Title clarified, a(6) corrected and a(7)-a(13) from _Aaron N. Siegel_, May 18 2022