cp's OEIS Frontend

A216581 Number of distinct connected planar figures that can be formed from n 1x2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree.

%I A216581 #34 May 30 2025 10:10:57
%S A216581 1,2,14,114,1038,10042,101046,1044712,11018478,117996288,1278942418,
%T A216581 13998440610,154462050186
%N A216581 Number of distinct connected planar figures that can be formed from n 1x2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree.
%C A216581 Figures that differ by a rotation or reflection are regarded as distinct (cf. A216492).
%H A216581 César Eliud Lozada, <a href="/A216492/a216492.jpg">Planar figures with up to 3 dominoes</a>
%H A216581 N. J. A. Sloane, <a href="/A056786/a056786.jpg">Illustration of initial terms of A056786, A216598, A216583, A216595, A216492, A216581</a> (Exclude figures marked (A) or (B))
%H A216581 N. J. A. Sloane, <a href="/A056786/a056786.pdf">Illustration of third term of A056786, A216598, A216583, A216595, A216492, A216581</a> (a better drawing for the third term)
%H A216581 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%H A216581 <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%e A216581 One domino (rectangle 2x1) is placed on a table. There are two ways to do this, horizontally or vertically, so a(1)=2.
%e A216581 A 2nd domino is placed touching the first only in a single edge (of length 1). The number of different planar figures is a(2) = 4+8+2 = 14.
%Y A216581 Cf. A056786, A216598, A216583, A216595, A216492, A216581.
%Y A216581 Without the condition that the adjacency graph forms a tree we get A216583 and A216595.
%Y A216581 If we allow two long edges to meet we get A056786 and A216598.
%K A216581 nonn,more
%O A216581 0,2
%A A216581 _N. J. A. Sloane_, Sep 08 2012, Sep 09 2012
%E A216581 a(4)-a(7) from _César Eliud Lozada_, Sep 08 2012
%E A216581 a(8)-a(12) from _Bert Dobbelaere_, May 29 2025