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.

1, 1, 3, 18, 139, 1286, 12715, 130875, 1378139, 14752392, 159876353, 1749834718, 19307847070

Offset: 0

Author

César Eliud Lozada, Sep 07 2012

Keywords

• nonn
• more
• nice

Comments

Figures that differ only by a rotation and/or reflection are regarded as equivalent (cf. A216581).

A216583 is A216492 without the condition that the adjacency graph of the dominoes forms a tree.

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

Examples

			One domino (2 X 1 rectangle) is placed on a table.
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.
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.
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.
		

Links

• C. E. Lozada, Illustration of initial terms: planar figures with up to 3 dominoes
• N. J. A. Sloane, Illustration of initial terms of A056786, A216598, A216583, A216595, A216492, A216581 (Exclude figures marked (A) or (B))
• N. J. A. Sloane, Illustration of third term of A056786, A216598, A216583, A216595, A216492, A216581 (a better drawing for the third term)
• M. Vicher, Polyforms
• Index entries for sequences related to dominoes

Crossrefs

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

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

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

Extensions

Edited by N. J. A. Sloane, Sep 09 2012

a(8)-a(12) from Bert Dobbelaere, May 30 2025