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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..7.

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

Example

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.

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.

Sequence in context: A275649 A199649 A357584 * A192406 A332664 A092639

Adjacent sequences: A216578 A216579 A216580 * A216582 A216583 A216584

Keyword

nonn,more

Author

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

Extensions

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

Status

approved