cp's OEIS Frontend

A216492 Number of inequivalent connected planar figures that can be formed from n 1 X 2 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 A216492 #72 May 30 2025 10:10:54
%S A216492 1,1,3,18,139,1286,12715,130875,1378139,14752392,159876353,1749834718,
%T A216492 19307847070
%N A216492 Number of inequivalent connected planar figures that can be formed from n 1 X 2 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 A216492 Figures that differ only by a rotation and/or reflection are regarded as equivalent (cf. A216581).
%C A216492 A216583 is A216492 without the condition that the adjacency graph of the dominoes forms a tree.
%C A216492 This is a subset of polydominoes. It appears that a(n) < A216583(n) < A056785(n) < A056786(n) < A210996(n) < A210988(n) < A210986(n), if n >= 3. - _Omar E. Pol_, Sep 15 2012
%H A216492 C. E. Lozada, <a href="/A216492/a216492.jpg">Illustration of initial terms: planar figures with up to 3 dominoes</a>
%H A216492 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 A216492 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 A216492 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>
%H A216492 <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>
%e A216492 One domino (2 X 1 rectangle) is placed on a table.
%e A216492 A 2nd domino is placed touching the first only in a single edge (length 1). The number of different planar figures is a(2)=3.
%e A216492 A 3rd domino is placed in any of the last figures, touching it and sharing just a single edge with it. The number of different planar figures is a(3)=18.
%e A216492 When n=4, we might place 4 dominoes in a ring, with a free square in the center. This is however not allowed, since the adjacency graph is a cycle, not a tree.
%Y A216492 Cf. A056786, A216598, A216583, A216595, A216492, A216581.
%Y A216492 Without the condition that the adjacency graph forms a tree we get A216583 and A216595.
%Y A216492 If we allow two long edges to meet we get A056786 and A216598.
%K A216492 nonn,more,nice
%O A216492 0,3
%A A216492 _César Eliud Lozada_, Sep 07 2012
%E A216492 Edited by _N. J. A. Sloane_, Sep 09 2012
%E A216492 a(8)-a(12) from _Bert Dobbelaere_, May 30 2025