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.

1, 2, 14, 114, 1038, 10042, 101046, 1044712, 11018478, 117996288, 1278942418, 13998440610, 154462050186

Offset: 0

Author

N. J. A. Sloane, Sep 08 2012, Sep 09 2012

Keywords

• nonn
• more

Comments

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

Examples

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

Links

• César Eliud Lozada, 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

a(4)-a(7) from César Eliud Lozada, Sep 08 2012

a(8)-a(12) from Bert Dobbelaere, May 29 2025