A216581 - OEIS

%I #34 May 30 2025 10:10:57

%S 1,2,14,114,1038,10042,101046,1044712,11018478,117996288,1278942418,

%T 13998440610,154462050186

%N 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 Figures that differ by a rotation or reflection are regarded as distinct (cf. A216492).

%H César Eliud Lozada, <a href="/A216492/a216492.jpg">Planar figures with up to 3 dominoes</a>

%H 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 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 M. Vicher, <a href="http://www.vicher.cz/puzzle/polyforms.htm">Polyforms</a>

%H <a href="/index/Do#domino">Index entries for sequences related to dominoes</a>

%e One domino (rectangle 2x1) is placed on a table. There are two ways to do this, horizontally or vertically, so a(1)=2.

%e 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 Cf. A056786, A216598, A216583, A216595, A216492, A216581.

%Y Without the condition that the adjacency graph forms a tree we get A216583 and A216595.

%Y If we allow two long edges to meet we get A056786 and A216598.

%K nonn,more

%O 0,2

%A _N. J. A. Sloane_, Sep 08 2012, Sep 09 2012

%E a(4)-a(7) from _César Eliud Lozada_, Sep 08 2012

%E a(8)-a(12) from _Bert Dobbelaere_, May 29 2025